Although not in Chelsea manager Frank Lampard's starting lineup, Pulisic came on after 55 minutes and took just five minutes to put his name on the scoreboard.
Chelsea made the stronger start to the game, with Giroud knocking in several dangerous crosses within the first 10 minutes.
The Blues' dominance made Kortney Hause's first Premier League goal all the more surprising when it came just before half-time.
Boasting 75% of the possession, Chelsea were unable to keep his right-footed shot out after a perfect cross into the box from Douglas Luiz.
Hause failed to get a clean attempt on it the first time, but Chelsea keeper Kepa spilled the ball, and Hause was there again to make sure it went in the second time.
With no changes for either side at half-time, Chelsea continued to dominate but failed to produce any clear chances for the first 15 minutes.
The introduction of the U.S. international proved to be the turning point for Lampard's side. In a carbon copy of the ball Luiz had dropped into the box for Hause's goal, Cesar Azpilicueta floated a ball into the box, and Pulisic struck it home from the back post.
Villa were left staggering when just two minutes later Giroud was given the space to turn and get a shot off that went flying past Nyland.
"We dominated, but it's the story of some of our games, we need to be more clinical," Lampard told Sky Sports. "But I can give the players some leeway because they've had a lot of time off. We showed great character and quality in the second half to win the game."
The win helps Chelsea cement their place in the top four, while Aston Villa remain in the relegation zone, two points from safety.