Goals from Mauro Icardi and Marcelo Brozovic either side of half time put the title hopefuls in control of the match, although Paolo Farago pulled a goal back with just under 20 minutes remaining to hand the hosts a glimmer of hope.
However, that was quickly extinguished as the in-form Icardi got his second of the game - and 15th of the season - to secure the points seven minutes from time.
The result sees Inter extend their unbeaten start to the season to 14 matches, lifting them one point clear of Napoli until at least Sunday, when their main title rivals take on Udinese with the chance to regain top spot.
The first half saw clear-cut chances at a premium for both sides, but Icardi made the most of a rare opening just before the half-hour mark when he swept a finish past the keeper after being found by Ivan Perisic's pullback.
Inter's lead was doubled 10 minutes into the second half when Antonio Candreva stole in behind the Cagliari defence down the right flank before cutting the ball back to Brozovic, who made no mistake when burying his finish into the bottom corner from the edge of the box.
Cagliari had won three of their previous four Serie A games heading into this match, though, and they refused to give up without a fight as Farago pulled one back with the pick of the bunch.
Leonardo Pavoletti's wicked cross from deep bent perfectly behind the defence to find Farago, who applied an equally impressive first-time finish to volley the ball into the corner.
It was not to be the beginning of a comeback for the hosts, though, and Icardi restored his side's two-goal lead to put the game to bed in the 83rd minute when he fired home from inside the box after Cagliari had made a mess of clearing their lines from a right-wing cross.
There was no way back for the hosts after that as Inter comfortably saw out the win, putting the pressure on the chasing pack when they play tomorrow having extended their unbeaten streak in Serie A to 16 games.