The France international began to make up for his struggles against Monaco by burying the first goal as the north Londoners moved back into third in the Premier League
After a disastrous performance against Monaco, the French striker got back on the horse by finishing off a low cross at a corner near the end of the first half.
Though Everton looked somewhat tired after their midweek Europa League exploits, David Ospina had to be in good form to fend off some good chances in the second half.
But Arsenal's holding-out paid off when Rosicky scored via a slight deflection from Phil Jagielka shortly before the end of normal time.
|VIEW FROM THE EMIRATES
|By Harry Sherlock
Arsenal have all three points and it is no less than they deserve. Everton simply didn't turn up in the first half, their early pressure fizzling out into a conservative, counterattacking display. Olivier Giroud opened the scoring with a superb volley before Tomas Rosicky rounded off the victory and Arsene Wenger will be pleased that there was no repeat of the Monaco debacle.
The players were applauded off the pitch as a carnival atmosphere took hold late on but Roberto Martinez must wonder what happened to his side. They threatened to spark into life after Aaron Lennon's introduction but it was a false dawn. They must improve or they will remain mired in the bottom half.
Arsenal might have fallen behind in the 17th minute if not for a piece of smart goalkeeping from David Ospina, who raced off his line to rob Romelu Lukaku of the ball after the striker had beaten Gabriel - in for Per Mertesacker as part of three changes from midweek - to a long ball over the top.
Giroud then spurned Arsenal's first chance as he turned Alexis Sanchez's near-post cross wide with a diving header but soon atoned for that miss to break the deadlock. The former Montpellier man converted Mesut Ozil's set-piece delivery with a cool first-time finish into the bottom-left corner six minutes before the interval.
Arsene Wenger's men gained confidence from that opener and went close to adding a second shortly afterwards when Santi Cazorla's long-range effort was tipped over the crossbar by Tim Howard, who was tested by his own player from the resulting corner as Muhamed Besic's attempted defensive header forced the American into a save.
Everton started the second half the stronger, though, and almost levelled in spectacular fashion as Gareth Barry sent a bicycle kick narrowly over the bar.
Lukaku provided Everton's main threat and only the acrobatics of Ospina prevented him from levelling matters.
Ospina dived brilliantly to his right to turn the Belgium international's shot over the target following a superb cross from Ross Barkley.
Substitute Aaron Lennon shot straight at Ospina and Ozil had an effort deflected wide at the other end before the German picked out Rosicky to settle matters. He fired home just seven minutes after coming on as Arsenal kept themselves in a strong position to return to the Champions League, despite a late point-blank miss from Giroud.