Neymar scored one goal and played a key role in the second as Brazil edged out Mexico in Samara to reach the World Cup quarter-finals for a seventh consecutive time. Brazil did not have it all their own way, especially in an opening period dominated by Mexico, but the five-time winners grew into what became a controlled performance. It means Mexico are once again eliminated at the last-16 stage – as they have been at every World Cup since 1994. His run across goal and clever backheel won Willian space, and the Chelsea midfielder only needed two touches to drive into box and lay the ball across for the world’s most expensive player to slide home.

Belgium completed a remarkable revival as they came from the World Cup abyss and beat Japan to reach the quarter-finals. Roberto Martinez’s side were trailing 2-0 when he brought on Marouane Fellaini and Nacer Chadli in the 65th minute, and Fellaini scored the equaliser before Chadli netted a 94th-minute winner. They now face Brazil in the last eight on Friday. Japan looked on their way to a famous win in Rostov after Genki Haraguchi ran onto Gaku Shibasaki’s long ball, which Jan Vertonghen should have cut out, to open the scoring. Takashi Inui’s 25-yard strike made it 2-0 and looked set to take the Asian side into their first quarter-final. Belgium’s Premier League stars – their golden generation – had put in a disappointing performance, and Martinez turned to the oft-ridiculed Fellaini and West Brom winger Chadli in his hour of need.

Their fortunes changed after that as Vertonghen scored a looping header to get them back into the game. Fellaini then headed in Eden Hazard’s cross to level before Chadli converted Thomas Meunier’s pass to finish off a flowing move and help the Red Devils avoid being the latest victims of a World Cup of shocks. Belgium are the first team to fight back from two goals down to win a World Cup knockout game since West Germany against England in 1970.

Sweden will play England in the quarter-finals of the World Cup after defeating Switzerland in a strangely compelling but untidy tie in St Petersburg. Emil Forsberg struck the decisive blow midway through the second half with a shot that deflected off the luckless Manuel Akanji and left Yann Sommer stranded in the Swiss goal. Sommer had brilliantly clawed away a shot on the turn from Marcus Berg in the first half and denied Haris Seferovic late on but it was undoubtedly a game that was more about missed opportunities than good saves.

England won a World Cup penalty shootout for the first time on a night of high drama in Moscow, overcoming Colombia to secure a quarter-final meeting with Sweden. Amid a fevered atmosphere inside Spartak Stadium, Eric Dier scored the winning kick after Jordan Pickford’s brilliant save from Carlos Bacca. England’s famous victory sets up a meeting with Sweden in Samara on Saturday, a game that can be seen live across the BBC. Southgate’s side looked to have emerged unscathed from an ill-disciplined match courtesy of Harry Kane’s penalty, only for Colombia’s Yerry Mina to equalise in the closing seconds of stoppage time to send the massed ranks of Colombia fans wild. The extra 30 minutes could not separate the sides and led to a nerve-shredding finale that has so often been England’s undoing, with a dismal record of just one win in seven shootouts at major tournaments before this.

England looked to be set for more agony when Jordan Henderson’s penalty was saved by David Ospina but Mateus Uribe smashed the following kick on to the crossbar to pave the way for Pickford and Dier to be England’s saviours. No previous world champions stand between England and the final. The winners of their quarter-final will face either Croatia or hosts Russia for a place in the Moscow showpiece on 15 July.

Kylian Mbappe announced himself on football’s biggest stage with two fine goals that gave France victory in a classic World Cup encounter with Argentina, and a place in the quarter-finals. Though much of the focus before the game was on Argentina superstar Lionel Messi, it was Mbappe who produced a brilliant performance that will linger long in the memory. Mbappe’s second-half double turned the game decisively in France’s favour, and inflicted more pain on Argentina in what may be their final chance to win the World Cup during Messi’s prime. In doing so, the 19-year-old became the first teenager to score two in a World Cup match since Pele netted twice for Brazil against Sweden in the 1958 final. Antoine Griezmann had already hit the bar with a free-kick by the time he put France ahead from the penalty spot in the ninth minute, following a searing Mbappe run that was ended by a clumsy Marcos Rojo foul.

Argentina looked unable to reply for much of the first half, until Angel di Maria hauled his side level with a stunning long-range curler shortly before the break. Thousands of raucous South American supporters were sent into raptures when Gabriel Mercado diverted a Messi shot past Hugo Lloris to give Jorge Sampaoli’s side the lead. But Benjamin Pavard’s stunning strike levelled the scores, and 11 minutes later Mbappe had scored twice – two clinical finishes that ensured the 2014 beaten finalists would be going home at the last 16. For the first he swept body and ball into space before driving past Franco Armani to score, while the second was swept in crisply at the end of a counter-attack as Argentina chased another leveller. Substitute Sergio Aguero did get a late consolation – a low header from a pin-point Messi cross in the 93rd minute.

Edinson Cavani scored two superb goals as Uruguay beat Portugal to set up a World Cup quarter-final meeting with France. Defeat for the European champions finished Cristiano Ronaldo’s hopes of success in Russia just hours after Lionel Messi and Argentina were knocked out, beaten 4-3 by Les Bleus. This World Cup has not been short of stunning goals and Cavani added another to the collection when he opened the scoring early on, playing a superb one-two with Luis Suarez before thumping home a header from his strike partner’s cross.

Uruguay had not conceded a goal at this World Cup before Pepe rose unmarked to nod in an equaliser from close range, prompting a brief spell of dominance for Portugal. But Cavani secured Uruguay’s place in the last eight – and a trip to Nizhny Novgorod to face France on Friday – when he steered a brilliant shot beyond goalkeeper Rui Patricio. The win may have come at a price, though, as Cavani limped off late on.

Hosts Russia pulled off the biggest shock of the 2018 World Cup so far as they beat 2010 winners Spain in the first penalty shootout of the tournament to reach the quarter-finals for the first time in 48 years. After extra-time ended with the score locked at 1-1, goalkeeper Igor Akinfeev was Russia’s penalty hero, denying Koke and then Iago Aspas to spark scenes of delirious celebration at Moscow’s Luzhniki Stadium.

His opposite number, David de Gea, got a hand to the first spot-kick he faced – from Fedor Smolov – but that was the closest he came to making a save as the Russians converted their remaining penalties in clinical fashion. Stanislav Cherchesov’s side, at 70 the lowest ranked team in the competition and 60 places below Spain, now face Croatia in the last eight in Sochi on Saturday.

Danijel Subasic saved three penalties as Croatia knocked out dogged Denmark in a nerve-shredding shootout to set up a World Cup quarter-final tie against hosts Russia. It came at the end of a largely disappointing tie – and one that had seen Luka Modric spurn a golden chance to snatch a late winner when his penalty shortly before the end of extra-time was superbly saved by Kasper Schmeichel.

The Leicester City goalkeeper also saved two penalties in the shootout at the Nizhny Novgorod Stadium but he could not prevent Ivan Rakitic slotting home the decisive 10th kick. Martin Jorgensen capitalised on the chaos caused by a long throw to fire a weak shot beyond Subasic in the opening minute. A scuffed clearance and an inadvertent header off Danish midfielder Martin Delaney left Mario Mandzukic with a good chance that he gobbled up, shooting beyond Schmeichel as Croatia soon levelled.