The Rossoneri made light of Zlatan Ibrahimovic's hamstring injury absence by restoring a five-point advantage over rivals Inter at the Serie A summit.
Captain Alessio Romagnoli was left unmarked to head a 17th-minute opener before Kessie converted from 12 yards following German Pezzella's lunging foul on Alexis Saelemaekers.
Kessie sent Bartlomiej Dragowski the wrong way in the 27th minute but the Fiorentina goalkeeper guessed correctly to gain a measure of revenge before half-time, Martin Caceres having brought down Theo Hernandez.
“I scored the first, I missed the second but I am going to take the third one,” Kessie said.
Ibrahimovic might have something to say about that on his return, despite chequered recent returns from the spot, and the evergreen striker was not the only high-profile absentee, with Milan head coach Stefano Pioli isolating at home after a positive coronavirus test.
Pioli spoke to his players via a video call to celebrate their victory and Kessie said: "He congratulated the team, he was happy. It was a very important game."
Coach Daniele Bonera took charge on the touchline in Pioli's absence and reserved praise for Kessie, who gained possession more times than any other Milan player (11), contested 16 duels, completed 85.3 per cent of his passes and had five shots in an all-action display.
“We know how important Franck is, he has become pivotal in terms of quantity and quality," Bonera told DAZN.
"We used to think he was mainly muscle, but he has really improved his technique and we are very happy with him."