Arsenal survived some second-half sloppiness and a valiant fight back from Brighton and Hove Albion to win 3-2 at the Amex Stadium and secure their place in the fifth round of the FA Cup. Theo Walcott and Mesut Özil both struck their first goals on return from injury to send Arsenal into a comfortable half-time lead, when an emphatic victory appeared on the cards. Instead it needed Tomas Rocisky’s second-half effort, either side of strikes from Chris O’Grady and Sam Baldock, to ensure that the holders’ name would be heading into the draw for the last 16. After four of the Premier League’s top six crashed out, and another still faces a replay against lower-league opposition, that the Gunners brought an end to a spectacularly unpredictable weekend of FA Cup action with a win over their Championship opponents will be cause for some relief for manager Arsene Wenger.

There was little sign of the drama to come in the early going. The gulf in class and the scale of the task in front of Chris Hughton’s side was laid bare inside two minutes. Walcott, in just his second start in a 12-month period wrecked by injury, got his first goal since New Year’s Day 2014 by slamming home a near-post cross by fellow Southampton graduate Calum Chambers. Just over 20 minutes later the visitors’ lead was doubled and the sizable Arsenal contingent to have made the journey south began to relax with the belief that their side wouldn’t be going the same way as Chelsea, Manchester City, Southampton or Tottenham, nor need a replay like Manchester United. This time it was Özil, only recently back from three months on the sidelines, who coolly struck just his second goal of the season and first since September.

The German’s strike was brilliantly set up by Rosicky, who, not for the first time in recent weeks, was the best player on the pitch. The Czech’s classy display was capped just before the hour mark by a clinical volley into the bottom corner from the edge of the box after a clever one-two with Olivier Giroud. It proved to be a decisive goal, too, with Brighton threatening a comeback that scarcely looked possible in the opening half. Otherwise isolated striker Chris O’Grady fired sweetly past an unmoved Wojciech Szczesny five minutes into the opening half to capitalize on some soft defending. And with 15 minutes remaining, Brighton struck again, this time after Baldock was allowed to run onto the end of a through ball and dink over Szczesny.

Brighton piled forward late on, and, although Arsenal survived, it was a second half that showed why Wenger is so intent on adding to his squad in the January transfer window. With Nacho Monreal replacing Per Mertesacker at the heart of defense and Mathieu Flamini coming in for Francis Coquelin, Arsenal were significantly short of the same defensive resilience they showed to win 2-0 at Manchester City a week ago.

Of course, it was a very different task in front of Arsenal this time around. Wenger’s team selection, while also providing a rest for some of his key performers this season, reflected that fact. Among the six changes to the starting 11, Walcott and Özil were brought in on the flanks. While lacking the defensive work rate of the men they replaced, they helped break through their tentative opponents.

Whereas City looked to take the game to Arsenal seven days ago, Brighton sat back and, to their great detriment in the opening period, gave far too much space to their opponents. To their credit, though, much of that was down to the incision in Arsenal’s play. Long before Brighton could even get a foothold in the contest, they were behind. Chambers did well to cross back from the byline and Walcott followed with a clean first touch and driven finish.

If Walcott had repeated that ruthlessness then Arsenal would likely have had the match put out of sight by halftime. On several occasions he failed to take advantage of opportunities when breaking through at pace. Still, it looked unlikely to prove costly when, in the 24th minute, Rosicky cut in unchallenged from the left and picked out Ozil with a wonderfully disguised pass to beat David Stockdale for a second time.

Arsenal were also denied a strong claim for a penalty when Brighton defender Bruno deflected the ball away from Walcott with his arm. But there was also a sign of the laxness that was to slip into Arsenal’s defending after the break. Laurent Koscielny this time escaped his dallying on the ball in his own box when Baldock’s finishing deserted him. Koscielny and Arsenal weren’t so fortunate in the second half. The French defender, along with Chambers and Flamini were at fault in failing to see off the danger from a ball into to box to allow O’Grady to give Brighton previously unimagined hope. And later Monreal was exposed as Baldock ran onto Jake Forster-Caskey’s pass and produced a far more composed effort than his first-half misfire.

But, despite a far more spirited performance form Brighton, Arsenal had just too much class. Fittingly then, it was the man who most exuded that quality, Rosicky, who inflicted the decisive blow to keep the holders very much alive.