Olivier Giroud and Arsenal keep up fight at top by beating Sunderland

Arsène Wenger had maintained that Olivier Giroud had the strength of character to rise above his off-the-field problems, that the centre-forward was one of those guys who found release from other matters when the intensity of the day job took over. Giroud proved him right here, as Arsenal did what they have done for almost the entire Premier League season: beat teams that they ought to be beating.

Giroud is hardly the first married footballer to be rumbled when sneaking a girl into his hotel room but the revelations over two Sundays earlier in the month came at a time when he was looking jaded on the field and the sense of personal crisis was strong enough for Wenger to leave him out of Wednesday's Champions League last-16 first-leg tie at home to Bayern Munich, which Arsenal lost 2-0. Giroud had also sat out last weekend's 2-1 home win over Liverpool in the FA Cup.

He returned against a Sunderland team who might be thriving in the cups but are dicing with their Premier League status and he was the principal reason why this game was effectively over by half-time. He scored two and laid on another for Tomas Rosicky as Arsenal offered an excellent impression in how to win without breaking sweat.

Arsenal scored two marvellous team goals – Rosicky's was a beauty – they were impressive across midfield and, also, supremely untroubled at the back but for Sunderland, the picture was somewhat darker. The manager, Gus Poyet, had suggested that his players were playing for their places in next Sunday's Capital One Cup final against Manchester City; this was an audition flunked. "Everything I had in mind for next weekend has gone," Poyet said. "I have to start again from zero."

Wenger claimed that he had omitted Mesut Özil because of a minor thigh problem rather than the Germany midfielder's own crisis, after the penalty miss against Bayern, but the issue was no more than a footnote. The only blots for Arsenal were the losses of the defenders Nacho Monreal and Laurent Koscielny to foot and back injuries respectively, although Wenger said neither was serious. "Both of them should be available next weekend [at Stoke City]," he said.

Jack Wilshere also felt tightness in his hamstring, with Wenger saying he was less sure whether "it's bad or not."

Arsenal always seem to be charged with offering a response or making some sort of statement but for Giroud, this was an important occasion. Whatever the whys and wherefores, the bottom line is that he was dropped for the glamour tie against Bayern and it would have hurt, particularly as his replacement was the untested 21-year-old Yaya Sanogo.

Giroud's bid for happier headlines was fired early on and the breakthrough was stamped with Arsenal's trademark passing. The ball was worked from right to left before Lukas Podolski provided the incision and the outstanding Rosicky flicked first-time for Wilshere. Phil Bardsley crashed into Wilshere only for the ball to squirt to Giroud and he tucked it away. The Frenchman beat his heart in the celebrations.

Arsenal bossed the possession and Sunderland were second best in every department, with Poyet lamenting his players' "poor technique, poor reading of the game, being second best on second balls and in sprints and power".

Podolski cut through the fancy stuff on the edge of the area with a thumping 25-yarder that worked Vito Mannone before Sunderland pressed the self-destruct button.

Mannone played the ball out to Santiago Vergini, the Argentinian centre-half who endured a hapless full Premier League debut, and he rolled it wide to Bardsley. It felt a bit tight as Bardsley played it back to Vergini and Arsenal pressed but Vergini's next decision mixed sloppiness and madness.

His back-pass was intended for Mannone but found only Giroud, and he slid home his 16th goal of the season almost apologetically.

Sunderland's supporters contended themselves with the knowledge that they were going to Wembley and whatever else would be, yet it threatened to get ugly for them when Arsenal carved out a masterpiece for the third. A blur of first-time passing, which was initiated by Rosicky, finished with him working a one-two with Giroud and clipping over the advancing Mannone.

Sunderland played for pride in the second half but things got worse when Koscielny powered a free header past the exposed Mannone. The corner had been conceded when Vergini sliced narrowly wide of his own goal. All Poyet could take was the way his players kept going. One substitute, Sebastian Larsson, fizzed a free-kick inches wide before another, Emanuele Giaccherini, beat Wojciech Szczesny with a lovely drive from distance.

But the afternoon belonged to one man. At full-time, Giroud embraced Mannone before taking the applause from all corners of the ground. "I had no hesitation about Olivier," Wenger said. "I wanted him to come back and be successful and he was."