Midfielder Houssine Kharja scored a scrappy goal early in the match, but Inter then spent the rest of the game defending desperately as Cagliari searched for an equalizer.
Daniele Conti and Davide Biondini came close and Andrea Cossu was a menace on the wing, but the Sardinians missed the finishing skills of Alessandro Matri, who was sold to Juventus during the transfer window.
Inter's goal was awarded to Inter defender Andrea Ranocchia, but was later given to Moroccan international Kharja after replays failed to show whether Ranocchia or Cagliari defender Michele Canini got the final touch from Kharja's shot.
"We played as well as we knew we could tonight," Inter fullback Maicon said. "In the first half it was a high tempo, but understandably that slowed down in the second."
Also Bologna needed a last minute header from Daniele Paponi to win 1-0 against 10-man Palermo, for whom Santiago Garcia was sent off.
At the San Siro both teams came out in determined manner and Inter striker Goran Pandev immediately went close with a long range shot that Michael Agazzi pushed away for a corner.
Inter's Julio Cesar then needed to be alert to stop Conti's header and Agazzi's quick reactions again stopped Pandev after the Macedonian found space to shoot.
Kharja opened the scoring in the seventh. Inter worked a quick freekick to the Moroccan. His first shot was blocked, but he was quick to the rebound and his shot across the face of goal was deflected in.
"We scored early on in the first half and I thought we would control the game, but we allowed Cagliari to go close to scoring," Inter coach Leonardo said. "We had a lot of trouble creating chances and closing out the match."
Cagliari hit back immediately and Biondini fired in a low shot that Cesar turned away for a corner.
Just before the halftime whistle Yuto Nagatomo flung himself at the ball to deny Biondini after Andrea Lazarri's charged down shot ran loose in the box.
In the 66th Nene took advantage of a Thiago Motta mistake to fire in a shot that Cesar saved. Inter's defense then crowded out the Brazilian as he was set to shoot following a goalmouth scramble.
"We were in more trouble than I expected," Leonardo said. "We were tired, but I don't want to use tiredness as an excuse."
