Arsène Wenger had contract news and in the absence of him finally confirming that he will prolong his 17½-year association with Arsenal beyond the end of the season, it was probably the next best thing. Tomas Rosicky, the manager said, had reached agreement on a new deal. Like Wenger, Rosicky's current terms are set to expire in June.

"Tomas Rosicky will stay," Wenger said. "We have an agreement with him and it will come out soon. I am absolutely adamant he has to stay at the club."

Rosicky's worth to Arsenal is lost on nobody who watches him regularly, least of all Wenger, who has come to reach for him in the very biggest matches like some sort of charm.

It was a surprise that he omitted him for Wednesday's Champions League last-16 first-leg defeat at home to Bayern Munich, but the Czech Republic international returned here and he was central to the over-running of Sunderland.

His goal was a beauty, stamped with Arsenal's first-time passing that slices through opposing teams when it is in sync, as it also was on Olivier Giroud's opener. Rosicky started the move, which took in contributions from Santi Cazorla and Jack Wilshere before he swapped passes with Giroud and clipped the ball over the advancing Vito Mannone.

It carried shades of Wilshere's goal against Norwich City from October and it technically made the game safe although, in reality, Arsenal were comfortable from the moment that Giroud turned the ball home after incisive work by Lukas Podolski, Rosicky and Wilshere.

Rosicky was billed as "Little Mozart" when he signed in May 2006 from Borussia Dortmund but the 33-year-old has evolved into the all-round midfielder who brings balance, organisation and urgency to the team.

"When he arrived, he was less a tactical player and more the Mozart from Prague," Wenger said. "He was purely a creative, offensive player. But today, he is a real organiser as well. He gives a real structure to the team.

"He is one of the players who plays the game of give-and-move and he is a great accelerator of the game. He always makes things happen, not with individual dribbling but with individual acceleration of his passing and his runs. His goal was one of the top goals we have scored."

Wenger was more forthcoming on Rosicky's contractual situation than he was about his own. When asked whether he could give any update concerning his longer-term future, Wenger replied that there was "nothing at all" before seeking to cut short the briefing. He has fudged the issue since last summer.

Wenger has never left it so late before re-signing and although Ivan Gazidis, the chief executive, has maintained a confidence that the Frenchman will commit to the continuation of another cycle at the club, there are those who question his motives for waiting. What if Arsenal were to win the title? Is Wenger leaving open the possibility of going out on a high? Does the decision even depend on a trophy?

The doubters, though, have been drowned out by the repeated suggestions, and not only from Gazidis, that Wenger is ready to sign. The manager has dropped a couple of hints himself, even if they have come in his carefully qualified language, and as good a time as any might be around the occasion of his 1,000th Arsenal game – the potentially pivotal league fixture at Chelsea on 22 March.

Arsenal's other ongoing contractual drama concerns the 31-year-old Bacary Sagna, whose deal also runs out in June. Wenger is happy to break the general club policy for 30-somethings and give the defender two more years but resolution remains some way away.

Sunderland return to north London on Sunday for the Capital One Cup final against Manchester City at Wembley and Gus Poyet can only hope that his players are more attuned to the occasion. "Sometimes, a good kick in the backside at the right time is good to wake you up," the manager said. "This game changed plenty of things in my mind."

Man of the match Olivier Giroud (Arsenal)