For once, the focus of north London did not fall on Arsenal on Sunday. After the week they've had, Arsene Wenger was happy to shun the limelight this time. Ask Gunners fans prior to kick-off if they'd rather three points or a Tottenham defeat in the Capital One Cup final and you'd have been greeted with differing opinions. As it happened, they all got their wish. Their arch-rivals lost to Chelsea at Wembley and Arsenal got their win — by the same scoreline, — courtesy of goals from Olivier Giroud and Tomas Rosicky, to move four points behind second-placed Manchester City. Olivier Giroud points to the sky after scoring the opener against Everton at the Emirates Stadium on Sunday . Giroud had a less than enjoyable time in his side's Champions League defeat against Monaco on Wednesday . The French striker congratulates team-mate Tomas Rosicky after he doubled the Gunners' lead on Sunday . But much like their demoralising Champions League loss to Monaco on Wednesday night, this didn't make for comfortable viewing. The 2-0 score doesn't tell the full story. This was unconvincing from Arsenal; the Emirates Stadium a bag of nerves until Rosicky's last-minute goal. Nevertheless, while their participation in this year's Champions League is under huge threat, their qualification for next year's competition remains on course. Despite their lack of fluency, Wenger would have been pleased with the response shown by his wounded players following the midweek loss. Giroud, barracked by his own supporters on Wednesday, did not hide; likewise Francis Coquelin, who played on after breaking his nose. This wasn't the Arsenal we're accustomed to, but after the Monaco monstrosity that didn't concern Wenger. 'I think what was really important was the mentally united response,' he said. Rosicky had been on the pitch for a matter of minutes when he doubled Arsenal's lead at the Emirates . Arsenal boss Arsene Wenger said he was proud of his side's response to the loss against Monaco . 'I am very proud of the response we have shown. Our defensive concentration was at a much higher level than on Wednesday. 'We know with the ball we can do better but overall what was important for us was to respond with a win. Not everyone can produce that after such a disappointment and it was vital for us to win.' Wenger's comments, particularly regarding his side's defensive stability, will have resonated with Per Mertesacker. The Frenchman rang the changes following Wednesday's loss. Vice-captain Mertesacker and Danny Welbeck were axed and replaced by Gabriel and Alex Oxlade-Chamberlain. For Gabriel, in particular, this was a huge opportunity. Per Mertesacker (right) was demoted to the bench following Arsenal's Champions League loss to Monaco . Giroud shows his strength in an impressive display to hold the challenge from Everton defender Phil Jagielka . Mertesacker's role in the starting XI has been called into huge question this season following a string of below-par displays, including against Monaco. On reflection, it wasn't the most convincing of performances from the 24-year-old on his first Premier League start since arriving for £13.5million from Villareal in January. A clean sheet is a clean sheet, though. Mertesacker knows that more than most. Gabriel very nearly gifted the visitors an early lead, failing to deal with a long-ball to allow Romelu Lukaku a free run at David Ospina. Thankfully for the Brazilian, his fellow South American bailed him out with some fine goalkeeping. A goal would not have flattered Everton, who started brightly. Arsenal, though, were lethargic. Giroud, unmarked from six yards, headed wide in the 28th minute after escaping the attentions of Phil Jagielka inside the penalty area. It was the last thing the striker needed after his wasteful display on Wednesday. But this time supporters didn't get on his back, responding to the miss by chanting his name. Arsenal's Gabriel (right) did not have the most convincing performance but managed to keep a clean sheet . Francis Coquelin was forced off after initially clashing heads with a team-mate before being hit in the face . This certainly had the desired effect, as the France international nipped in front of John Stones to flick home Mesut Ozil's corner in the 39th minute. Gareth Barry tried, spectacularly, to put Everton level but his acrobatic bicycle kick flew over. Kevin Mirallas then saw a penalty appeal rejected by Andre Marriner, after claiming Oxlade-Chamberlain had handled. Much like the first half, Roberto Martinez's side made a positive start after the break — Luke Garbutt's dead-ball delivery causing Arsenal's defence problems. Aaron Lennon, given his Spurs connections, was afforded a horrendous welcome when introduced in the 62nd minute. There would have been greater boos three minutes later had Ospina not tipped over Lukaku's first-time shot from a Barkley cross. It was even more uncomfortable for Coquelin (below), who was left with a broken nose following an accidental collision with Giroud. Luke Garbutt attempts to drive down the win but his progress is stalled by Arsenal defender Hector Bellerin . Lennon missed a glorious chance to ram Arsenal supporters' insults down their throats, firing straight at Ospina after great work from Seamus Coleman. The stadium was a bag of nerves by this point. Ozil should have eased the tension in the 80th minute after being sent clean through on goal by Oxlade-Chamberlain but the German's shot was blocked by Jagielka, before substitute Rosicky struck in the final minute to ensure Wenger could finally relax.
Arsenal striker Olivier Giroud scored the opener versus Everton on Sunday . Frenchman responded well following his wasteful show against Monaco . Tomas Rosicky's finish helped the Gunners to go on to beat the Toffees 2-0 . READ: Giroud responded well after Monaco defeat, says Arsene Wenger . CLICK HERE for all the latest Arsenal news .