Croatia striker Kalinic has struggled badly for his best form since joining Milan from Fiorentina last August and he was without a goal in 2018 for the Rossoneri when he came off the bench midway through the second half on Sunday.
He missed a gilt-edged headed chance after Matteo Politano's 75th-minute opener for the relegation-threatened visitors but Kalinic latched on to Mateo Musacchio's cross and turned to fire into the roof of the net with four minutes to go.
Milan head coach Gennaro Gattuso signed a contract extension until 2021 this week and the work ethic he has successfully instilled in the squad was again in evidence as they tore at Giuseppe Iachini's side from the first whistle.
However, they lacked for precision, with Franck Kessie's barely explicable early miss setting an unwelcomely wasteful tone.
Milan lie sixth in the table, in the final Europa League qualification spot, seven points behind rivals Inter – defeated 1-0 at Torino earlier on Sunday - and eight shy of Roma and Lazio in the third and fourth Champions League places.
Roma's conquerors Fiorentina are two points further back in seventh, while Sassuolo are 14th – three points clear of third-bottom Crotone.
Milan made a rapid start and Kessie should have headed them into a first-minute lead but met Ricardo Rodríguez's excellent cross with his chest and Sassuolo goalkeeper Andrea Consigli managed to claw to safety.
An injury to Alessio Romagnoli forced an early change in the Milan defence, with Musacchio introduced, but much of the action was concentrated at the other end of the field as Consigli worked his way through a virtuoso showing.
The visiting goalkeeper pushed over Hakan Calhanoglu's rising shot from the edge of the box and got down to beat away a testing free-kick from the Turkey international before keeping out Suso's curling 25th-minute attempt from the right.
There was more to come as Kessie was twice thwarted by another former Atalanta man – Consigli standing firm to block at his near post and repelling the Ivory Coast midfielder's follow-up with his legs.
Early in the second half, the Rossoneri appeared to be running out of ideas as increasingly desperate goal attempts flew off target or were met with blocks.
Sassuolo substitute Antonino Ragusa scooted around Lucas Biglia in the 64th minute, only to lose his footing and shoot too close to Gianluigi Donnarumma.
Warning signs were not heeded and a loose defensive header from Leonardo Bonucci was anticipated by Luca Mazzitelli, who laid on the alert Politano to finish with aplomb from the edge of the box.
5 - Matteo #Politano has scored five goals in the current league season, equaling his best Serie A season in terms of goals (2016/17 and 2015/16). Scorer. #MilanSassuolo — OptaPaolo (@OptaPaolo) April 8, 2018
An unsatisfactory conclusion to the match got worse for Bonucci as a booking for dissent ruled him out of next weekend's trip to title-chasing Napoli, but Kalinic took centre stage.
There were jeers when he missed badly from Calhanoglu's delightful cross and there was more than a touch of frustration in the vicious 86th-minute equaliser that followed.
Giacomo Bonaventura thought he had won it with a rasping stoppage-time strike but there was one more act of heroism from Consigli.
Key Opta stats
- Milan have drawn two games in their last two Serie A matches, as many as they drawn in their previous 14.
- Gennaro Gattuso's side are unbeaten in six home league games in a row (W4, D2) for the first time since January 2017.
- Sassuolo are unbeaten in their past five Serie A games (W1 D4).
- Mateo Musacchio has provided tonight his first assist for AC Milan in all competitions.
- Milan attempted 35 crosses, a record for them in a match this season.
- Francesco Acerbi started tonight the 100th Serie A game in a row for Sassuolo.