Milan moved level on 16 points alongside second-placed AS Roma as goals either side of the break from Juraj Kucka and M'baye Niang and an own goal from Dario Dainelli in the dying seconds ensured their victory.
Yet Inter suffered a wretched afternoon at the San Siro as Icardi, already embroiled in controversy over criticism he had made of the club's hardcore fans in an autobiography, missed a penalty during the defeat.
Some ultras, who have called for leading scorer Icardi to be stripped of the captaincy, even cheered and jeered after the miss and the Argentine's future at the club looks uncertain.
Despite his miss at 0-0, Inter looked poised to close in on the top spots with a win once Joao Mario scored after 56 minutes.
Yet Cagliari pulled level through forward Federico Melchiorri in the 71st minute before an own goal by keeper Samir Handanovic, who turned Melchiorri's low cross into his own net, consigned Inter to the loss that leaves them 11th on 11 points.
Lazio striker Ciro Immobile scored a penalty with the very last kick of the game to rescue a 1-1 draw against Bologna and make amends for a string of wasted chances throughout the game.
Immobile scored in the seventh minute of stoppage time after Bologna had taken the lead when Filip Helander, on loan from Verona, connected with a free kick to turn the ball in after 10 minutes.
Lazio reacted with Italy international Immobile hitting the post with a shot after half an hour and having another effort cleared off the line.
It was an even more one-sided affair after the break with the visitors' keeper -- Angelo Da Costa -- making a sensational reflex save to deny Sergej Milinkovic-Savic from close range.
A Milinkovic-Savic cut-back was then turned goalwards by a Bologna defender, but goalline technology showed it had not fully crossed the line when Da Costa once again came to the rescue to palm it away.
The Brazilian keeper was eventually beaten when Immobile converted from the penalty spot at the end of the game to rescue a point for the hosts.
The result leaves Lazio in fifth place on 14 points level with Napoli, who lost 3-1 to AS Roma on Saturday.
Juventus are top on 21 after their 2-1 win over Udinese on Saturday.
(Reporting by Karolos Grohmann; Editing by Toby Davis and Ian Chadband)
