France international Giroud poked Milan level with 15 minutes remaining of a thrilling encounter after Ivan Perisic had given champions Inter a deserved first-half lead with a perfectly placed volley from Hakan Calhanoglu's corner.
And three minutes later the 35-year-old sent the Milan fans at the San Siro wild with a neat turn and low finish after collecting Davide Calabria's pass.
"We were in difficulty for the first half. The second 45 minutes we got back in the game, and I was hoping for one or two chances in the area," Giroud said to DAZN.
"The first was a bit lucky but the second was a good ball from Cala (Davide Calabria) and great for our fans... I don't know what to say. I'm very happy and proud of this team which never gave up."
Giroud was only playing because Zlatan Ibrahimovic was out with an Achilles tendon injury but pounced just as Inter looked to be headed for what up to that point would have been a deserved win.
Milan had hardly created anything until Giroud pushed Brahim Diaz's mishit and deflected shot past Samir Handanovic but are now right back in a title race which seemed to be heading in Inter's favour.
Napoli can pile even more pressure on Simone Inzaghi's Inter, who have a game in hand, when they face Venezia on Sunday with the chance to pull level on 52 points with Milan.
Inter travel to Napoli next weekend in a huge fortnight for them which also includes the visit of Liverpool for the first leg of their Champions League last 16 tie.
The defeat will be deeply disappointing for Inter, who were by far the better team for much of the match, and if it hadn't been for Mike Maignan could easily have been a couple of goals ahead by the time Giroud struck.
France stopper Maignan prevented Denzel Dumfries from putting away a simple one-on-one chance in the first half and kept Milan in the game long enough for them to inflict on Inter a first league home defeat since October 2020.
"It was one-way traffic for 70 minutes... If we played the match again 10 times we might lose once," said Inzaghi.
"We didn't deserve to lose, but that's football."
Furious Zaniolo denied
Jose Mourinho said Roma were seen as "small" by Italy's footballing powers after Nicolo Zaniolo was denied a last-gasp winner in his team's goalless draw with 10-man Genoa which leaves their already slim Champions League hopes hanging by a thread.
Zaniolo, considered one of Italy's most talented players, crashed home a powerful low finish from the edge of the area in the 91st minute at the Stadio Olimpico and then charged towards the wildly celebrating home supporters.
However the fans' cheers turned to jeers when, after an on-field review by referee Rosario Abisso, Tammy Abraham was judged to have committed a foul when he stepped on Johan Vasquez's foot in the build-up, leaving Roma four points behind fourth-placed Atalanta having played two games more.
Zaniolo, 22, was then sent off for his protests at the decision and had to be held back after the final whistle by Mourinho, who was livid after his 100th match as a Serie A coach ended in controversy.
"Roma are small in the eyes of the powerful... That red card is not being shown to Lautaro at the San Siro, or (Giorgio) Chiellini or Zlatan," Mourinho told reporters, insisting his player had not personally insulted the referee.
Roma are seventh, three points away from fifth-placed Juventus who host Verona on Sunday night with new boy Dusan Vlahovic set to make his debut for the 36-time Italian champions.
Vlahovic's former team Fiorentina slumped to a 3-0 home defeat at the hands of Lazio, who moved above Roma into sixth thanks to second-half goals from Sergej Milinkovic-Savic and Ciro Immobile and Cristiano Biraghi's late own goal.
