Atalanta played most of the match a man down after goalkeeper Pierluigi Gollini saw red after 22 minutes at the Mapei Stadium.
Luis Muriel missed a late penalty that could have given Atalanta a win that would have put Inter's celebrations on hold but the second-placed Bergamo side are now 13 points behind Inter with four games remaining.
Inter, who beat Crotone 2-0 on Saturday, denied Juventus a 10th straight league title with Andrea Pirlo's side now fighting for a Champions League spot.
Juventus president Andrea Agnelli congratulated his Inter counterpart Steven Zhang on the Chinese-owned club's success.
"Well done Steven! Happy for you and proud of being your loyal opponent on the pitch and friend off the pitch. We'll be back," Agnelli wrote on Twitter.
Atalanta are equal on 69 points with third-placed AC Milan, who beat Benevento 2-0 on Saturday, and two points ahead of Napoli, who were held 1-1 at home against Cagliari.
Juventus are fifth before they play later Sunday at Udinese.
In Emilia-Romagna, Robin Gosens scored 10 minutes after Gollini's sending off for recklessly bringing down Jeremie Boga.
Domenico Berardi pulled Sassuolo level from the penalty spot seven minutes after the break after Hamed Traore went down in the penalty box under pressure from Rafael Toloi.
Sassuolo also played the final quarter of an hour a man down after Brazilian defender Marlon was sent off for a second yellow card, but goalkeeper Andrea Consigli saved Muriel's penalty.
In Naples, Nahitan Nandez got a late equaliser for Cagliari to cancel out Victor Osimhen's 13th-minute opener.
Napoli are still in the running for the Champions League while Cagliari move one point clear of the relegation zone.
Lazio also stayed in the Champions League chase with a thrilling 4-3 win over Genoa for a club record 11th consecutive win.
Joaquin Correa scored a brace, breaking the deadlock after half an hour and striking again 11 minutes after the break.
Ciro Immobile added the second from the penalty spot before half-time after an Ivan Radovanovic foul.
Genoa made a triple substitution after the break and got back into the game when under-pressure Lazio defender Adam Marusic turned into his own net.
Luis Alberto curled in a third for the hosts just after with Correa then making it 4-1.
The hosts survived a late scare as Genoa fought back with Gianluca Scamacca slotting in a penalty with 10 minutes to go and Eldor Shomurodov blasting in another goal almost immediately.
