Arsenal boss Arsene Wenger says he is not worried about losing Alexis Sanchez in January despite the forward scoring twice as the Gunners won at Crystal Palace. After Andros Townsend cancelled out Shkodran Mustafi’s first-half opener, Sanchez struck twice in four minutes. The Chile forward squeezed a clinical strike in at the near post to make it 2-1 before bringing Jack Wilshere’s superb ball from his own half under control and flicking into the net. James Tomkins headed in late on but Sanchez’s double was enough to secure a win that keeps sixth-placed Arsenal level on points with Tottenham, who are fifth, and one point behind fourth-placed Liverpool.

Sanchez’s contract expires at the end of the season and the 29-year-old has been linked with a move to league leaders Manchester City, who failed in their bid to sign him in the summer. After three draws and just one win from their four previous Premier League outings, this was arguably an important game for the Gunners in their bid to remain in the hunt for a top-four finish, especially after wins for rivals Tottenham, Liverpool and Chelsea in midweek. They started the day with six points fewer than they had at the same stage last season – and Wenger’s side ultimately finished outside the Champions League places – so a positive result and performance was needed to help ease any Arsenal fans’ concerns their campaign was in danger of fizzling out.

For large periods, the performance was certainly there. The visitors often produced some of their best attacking play of the season, particularly in the first half when Palace could not cope with short, intricate passing that time and again opened up the defence. But their inability to finish off the many opportunities they created meant their opponents always had a chance to get back into the game. That proved the case early in the second half when Zaha’s cross caught Arsenal’s defence asleep and Townsend struck. A five-minute spell of Arsenal disarray followed and the Gunners could easily have found themselves falling behind, but Sanchez – so often Arsenal’s saviour – settled the nerves with two moments of quality.

But even with a two-goal cushion Arsenal were never at ease, and Wenger’s concern about his side’s defensive frailties was highlighted by his decision to replace striker Lacazette with Francis Coquelin late on. That was still not enough to prevent Palace from reducing the deficit to one, setting up a tense finale.

Roberto Firmino’s powerful finish earned Liverpool a draw in an incredible Premier League encounter that had seen Arsenal score three goals in just five second-half minutes. The Gunners had been trailing 2-0 after Philippe Coutinho scored his first headed league goal in England before Mohamed Salah added a second early in the second half with a deflected strike. But Arsenal suddenly came alive as Alexis Sanchez headed in Hector Bellerin’s cross from close range before Granit Xhaka’s thumping strike was too powerful for Simon Mignolet’s weak save. Barely two minutes later Mesut Ozil put Arsenal ahead with a neat clip over Mignolet.

Play swung from one end of the pitch to the other at blistering pace, with both sides looking capable of scoring with every attack. But it was Liverpool who had the final say in one of the most thrilling Premier League encounters in years as Petr Cech could only take the sting out of Firmino’s shot and the ball bounced over the line. The point meant Liverpool held onto fourth place, with Arsenal remaining fifth – a point behind the Reds. This had looked like being a routine win for Liverpool after a dominant first half. They led through Coutinho’s clever header and should have had more but for some uncharacteristically wasteful finishing by Sadio Mane and Salah. However, it was not long until the Premier League’s top scorer had his 15th of the season, and so began an incredible six minutes…

52 mins: Salah races on to Firmino’s superb pass and makes it 2-0 with a deflected finish. Arsenal, who have not had a single shot on target, look beaten.

53 mins: Out of nowhere, Arsenal are back in it. Sanchez is well placed to nod in Bellerin’s cross from close range.

56 mins: What’s going on!? Arsenal are level! Xhaka tries his luck from 25 yards and the ball fizzes through Mignolet’s hand.

58 mins: Goals! Goals! Goals! Arsenal are ahead as Ozil is on to Alexandre Lacazette’s backheel before clipping the ball over Mignolet.

The Gunners were no doubt helped by Liverpool’s poor defensive performance, but Arsene Wenger praised the character of his side to stage such a fightback.

Manager Arsene Wenger says Arsenal cannot afford further injuries over the busy Christmas period after striker Olivier Giroud suffered a hamstring problem in their Carabao Cup quarter-final win over West Ham. Wenger, who made 11 changes from the weekend triumph over Newcastle, saw his side struggle to break down the defensively resolute visitors in the first half. But England forward Danny Welbeck broke West Ham’s resistance just before the break, turning in Mathieu Debuchy’s header across goal as the hosts stayed on course for a first League Cup win since 1993.

The Gunners’ night was soured by the loss of Giroud to an injury that could rule him out for three weeks, while Francis Coquelin also limped out of the match late on. With Arsenal embarking on a run of 10 games in 36 days, Wenger admitted the loss of Giroud had come as a blow. West Ham boss David Moyes also named a much-changed side but they failed to click in attack, with the belated introductions of Andy Carroll, Diafra Sakho and Marko Arnautovic unable to undo the home defence. Neither Joe Hart, restored to the West Ham side for the rested Adrian, nor Arsenal’s second-choice goalkeeper David Ospina were forced into much action in what was a disjointed contest.

Moyes’ side had been content to sit back and try to catch Arsenal on the counter during a low-quality first half, but even with the attacking changes they could not muster a single shot on target. Arsenal will face Chelsea in the semi-finals. The Blues host the first leg in the week commencing 8 January. The second leg is two weeks later. Manchester City and Bristol City meet in the other semi.