The Frenchman's first-half double and strikes from Tomas Rosicky and Laurent Koscielny ensured the Gunners kept pace with leaders Chelsea, who won at home to Everton earlier in the day.
Any lingering doubts Arsenal may have had after the midweek loss to Bayern Munich were eased when Giroud opened the scoring after just five minutes.
He owed the goal to the skill and craft of Jack Wilshere in the build-up, with the England midfielder exchanging passes with Tomas Rosicky before elegantly gliding past several defenders and teeing up an unmarked Giroud to slot home from close range.
Lukas Podolski went close with a shot from distance not long after, but it took until the half hour mark before Giroud scored his second, as Sunderland gifted the France striker the chance to score.
Goalkeeper Vito Mannone rolled the ball out to a defender before Santiago Vergini under-hit a back pass that Giroud pounced on to score.
Sunderland were at sixes and sevens at the back, and it came as little surprise when Rosicky made it three just moments before half time.
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Wilshere, Santi Cazorla and Giroud neatly passed the ball through the visitors with ease, before the Czech finished off from close range to cap a wonderful team goal.
Black Cats boss Gus Poyet made two changes at the break with Seb Larsson and Ignacio Scocco replacing Adam Johnson and Jozy Altidore, and that changed almost paid off as Fabio Borini got clear to test Wojciech Szczesny with an angled drive.
However the game was up in the 57th minute as Koscielny evaded his marker to head home a Cazorla corner.
Emmanuele Giaccherini earned an 81st minute consolation for the visitors as he curled home after a Szczesny punch clear fell straight to his feet.
