AC Milan dominated at San Siro to gain a victory that sent them provisionally into first place on 38 points against the bottom-placed Salernitana
Kessie guided a finish into the bottom corner after five minutes and Saelemaekers struck after 18 minutes to give the hosts a comfortable lead.
Belgian Saelemaekers showed his support for injured teammate Simon Kjaer, who was ruled out for six months on Friday after knee surgery, by running to the bench and lifting Dane’s shirt to celebrate his goal.
Stefano Pioli’s side recovered from back-to-back league defeats by beating Genoa on Wednesday and continued their return to form with a controlled performance against Serie A’s basement side.
Rafael Leao raced down the wing and cut across into Kessie’s path for a cushioned finish, and Brahim Diaz almost made it two when his effort clipped the outside of the post.
Kjaer’s injury was a big blow for Milan this week and they had more bad news when striker Pietro Pellegri, making his first start of the season, was forced off after 15 minutes.
But Saelemaekers soon put smiles back on the home crowd’s faces by curling a shot into the bottom corner, becoming the 14th Milan player to score in the league this season, the highest number for one club in the division.
The hosts had chances to extend their lead, with goalkeeper Vid Belec producing good saves to deny Rade Krunic and Junior Messias and Diaz firing wide from 12 yards out as the Rossoneri mustered 22 attempts.
Milan’s current points tally of 38 is their highest after 16 league games since 2003/04, when they won the title.
“We need to forge our own path and play with this determination”, Milan defender Alessandro Florenzi said.
“It is not about sending messages to the other teams; we only have to put pressure on ourselves. When we play under pressure, we do better. We aren’t looking too far ahead”.
Napoli will be looking to reclaim top spot when they host Atalanta on Saturday night. The visitors, meanwhile, could close the gap to first place to four points with a win.