Chelsea now boast a four-point lead on both fourth-placed Leicester and United in fifth, though both those teams have an extra game left to play after 1-0 win against Norwich City.
On another night Giroud could have had four, but in the end his solitary headed goal could wind up finally pushing the Blues into next term's Champions League.
Ajax signing Hakim Ziyech was in the stands to watch his new team-mates, with the Morocco forward already training with the Blues ahead of being available for action next term.
Right at the death of the first-half, Giroud put paid to a hugely frustrating 45 minutes.
The continually outstanding Pulisic had drifted onto the left wing, checked back onto his right foot - and delivered a sumptuous cross.
Giroud had precious little option other than to nod the Blues into the lead.
And how the Frenchman toasted that goal with relish, exchanging high fives and fist bumps with Jorginho.
Because in everything that came his way before his goal, Giroud had botched, and in some style.
