The France international, whose last goals came when he hit a hat-trick against Aston Villa on the final day of last season, turned in Kieran Gibbs' cross 19 minutes from time before glancing in a corner to seal a fourth away league win in a row for the Gunners.
Alexis Sanchez had put Arsenal ahead with a fine first-half header, and Mesut Ozil and Alex Oxlade-Chamberlain were both guilty of missing one-on-one chances to double that advantage.
Sunderland, who came into the match without a league win under David Moyes, grabbed an equaliser after 65 minutes when Jermain Defoe converted from the penalty spot following a Petr Cech foul.
Giroud, who made his return from injury against Reading in the EFL Cup in midweek, put Arsenal back in front two minutes after coming on before netting a second just five minutes later to take his tally to seven goals in seven games against Sunderland.
Sanchez added a fourth with 12 minutes to play to resounding boos from the home fans who began to file out of the Stadium of Light, as the visiting faithful celebrated a win that puts Arsenal temporarily three points clear at the top of the table.
Arsenal started the better of the teams and Jordan Pickford twice rescued his side following slack defending, denying Ozil from close range before blocking at the feet of the charging Francis Coquelin.
But Pickford could do nothing to stop Sanchez giving Arsenal the lead on 19 minutes as the home side's poor concentration was punished.
Oxlade-Chamberlain burst past Duncan Watmore down the right and curled a cross towards the penalty spot, and Sanchez raced in front of the static Lamine Kone to steer a fine header into the far corner.
Defoe was denied an equaliser when Wahbi Khazri was flagged offside before cutting back for the striker to turn home, though Alex Iwobi then almost doubled the lead with a dipping effort from 20 yards.
Pickford did well to snatch an Ozil lob from the air, but Sunderland's task became even tougher when captain John O'Shea - making his 350th Premier League start - was forced off with a hamstring injury just before half-time.
Oxlade-Chamberlain dragged a poor shot wide on the break for the Gunners, but Sunderland started the second half with greater resolve.
Sanchez felt aggrieved not to win a penalty when he went to ground easily after tumbling under pressure from Kone, and just minutes later, Sunderland found themselves level.
Shkodran Mustafi misjudged a bouncing ball to allow Watmore to drive into the penalty area, and after the onrushing Cech tripped the 22-year-old with his head, Defoe swept high into the net from the spot with Sunderland's first shot on target.
Arsene Wenger responded by introducing Giroud, and the 30-year-old wasted little time in making an impact, steering a low left-footed finish beyond Pickford after Gibbs' clever cross from the left.
Giroud glanced Ozil's corner up and over Pickford into the far corner five minutes later, before Sanchez added gloss to the scoreline as he collected a rebound from the returning Aaron Ramsey before turning around Pickford and slotting home.
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