Francesco Acerbi took advantage of some lax Milan defending to head the Nerazzurri into the lead inside the opening 20 minutes.
After spurning several chances to double their advantage, Inter finally grabbed a deserved second through Marcus Thuram's 49th-minute effort.
Fikayo Tomori pulled a goal back in the closing stages to set up a nervy finish before tensions spilt over in stoppage time as Theo Hernandez, Denzel Dumfries and Davide Calabria.
Inter saw out the remaining moments to clinch a famous derby win and seal their first Scudetto since the 2020-21 season.
As for Simone Inzaghi, he can celebrate his first Serie A title as manager, adding to the three Coppa Italia trophies and five Italian Super Cups he has already won during his coaching career.
Acerbi gives Inter an early lead
With the title in their sights, the Nerazzurri required just 18 minutes to hit the front against their city rivals at San Siro.
Federico Dimarco's near-post corner was met by Benjamin Pavard, whose neat flick-on allowed an unmarked Acerbi to head home his third goal of the season.
Serie A top scorer Lautaro Martinez then spurned a gilt-edged opportunity, sending the ball high and wide from Dimarco's low cross.
After being put under significant pressure, Milan finally offered a meaningful goal threat just before the half-hour mark, with Rafael Leao's driving his left-foot strike at Yann Sommer.
Inter should have added a second when Nicolo Barella teed up Marcus Thuram, but the French strike could only guide his strike wide of Mike Maignan's goal.
Maignan's opposite number was then required to make a fine stop to deny Calabria from scoring his first goal of the season.
Inter launched an incisive counterattack from Sommer's superb save to create the opening for Henrikh Mkhitaryan to sting the palms of Maignan.
Inter prevail to clinch Scudetto
The Nerazzurri may have missed the chance to double their advantage before the break, but they needed just four second-half minutes to beat Maignan for a second time.
Thuram drove inside from the left flank before picking out the bottom corner with a driven shot from the edge of the box.
Leao attempted to quickly halve the deficit, but his powerful strike was ultimately kept out by a diving Sommer.
The contest appeared to be petering towards its conclusion until Tomori nodded home after Sommer had pushed Matteo Gabbia's header onto the post.
With momentum in their favour, Noah Okafor went close to finding an equaliser, only to see his prodded effort cleared off the line.
The emotions ultimately boiled over in stoppage time as Hernandez and Dumfries received their marching orders for their involvement in a melee, before Calabria saw red for striking Davide Frattesi in the face.
Following a dramatic conclusion, referee Andrea Colombo blew the final whistle to signal the end of Inter's successful title bid.
While Inter will celebrate winning the title against their rivals, the pressure will mount on Milan boss Stefano Piolo after overseeing a Europa League exit and a derby defeat in the last two games.