The Frenchman came off the bench to notch a double and help secure a 4-1 win for the Gunners at the Stadium of Light.
Fellow forward Alexis Sanchez also scored twice while Jermain Defoe had levelled the game at 1-1 from the penalty spot.
Despite a lopsided scoreline, Giroud insists it was far from easy on Wearside and played down his strikes, claiming he would be ‘Superman’ if he could replicate them every week.
“At the end we made it look easy but it was totally the reverse,” Giroud said. “We started well, they came back well and we didn’t put them away.
“We were exposed in the second half so it was nice to score the second. It was nice to finish the job.
“If I could do that every single game I would be Superman. I had a great assist from my team-mates so I had to finish the job. This is big for me, coming back from a tough injury, so I’m happy to be back.”