Antonio Conte’s men rallied from two goals down to stun Stefano Pioli’s side 4-2 and move above Juventus to the top of the Serie A table.
Zlatan Ibrahimovic provided the assist of Ante Rebic’s opener after 40 minutes before the big Swede headed in his second league goal for Milan since rejoining from LA Galaxy on the cusp of half-time.
However, two quick goals after the break from Marcelo Brozovic and Matias Vecino brought Inter back into the game before Stefan de Vrij and Romelu Lukaku added further goals to complete the remarkable comeback.
Lukaku was full of praise for his team after the game as Inter bid to win the Serie A for the first time in ten years.
"We did really well during the second half. They played well during the first half, as we left them too much space and we struggled," Lukaku, who netted his 17th league goal of the season to complete the scoring in stoppage time, told Sky Sport Italia.
"However, we came out well after the interval. We completed the comeback and we're delighted with the win. I think that everyone has seen this team's mentality, we never give up and we're always looking to win.
"I'm here to win and my only aim is to help the team get results. I want to thank all of the fans, my team-mates, Mister [Antonio] Conte and all of his backroom staff for the support that they're giving me."
Lazio’s victory over Parma on Sunday means the top three teams in Serie A are separated by a single point.