After a largely frustrating season, Roberto Mancini's men have hit their stride in recent weeks and secured a third straight win with a disciplined performance in Sardinia.
Mateo Kovacic opened the scoring in the 47th minute with a composed strike from just inside the area.
Icardi has been one of Inter's brightest sparks this season and he again lit up this contest, cutting in from the right and curling a fierce shot beyond Zeljko Brkic in the Cagliari goal.
On-loan Inter forward Samuele Longo pulled one back for Cagliari from long range six minutes later but, despite coming under significant pressure in the closing stages, the visitors hung on to maintain their recent momentum.
The German then headed wide at the near post before Brozovic's low shot was well saved by Brkic, with Icardi's close-range follow-up blocked.
For all Inter's possession and relative control of the game, they would have fallen behind in the 36th minute if not for a strong piece of defending from Davide Santon.
The on-loan Newcastle United defender cleared off the line after goalkeeper Juan Pablo Carrizo could only deflect Duje Cop's point-blank effort into his path.
But the visitors' persistence paid off shortly after the restart as Kovacic slotted home with a cool side-foot finish after Cagliari had failed to deal with a long ball into the box.
Cagliari responded well, however they could not take advantage of some extremely haphazard Inter defending, Andrea Cossu unable to capitalise on Nemanja Vidic's error before Carrizo denied Paul-Jose M'Poku and substitute Longo.
And Cagliari's profligacy was punished by Icardi, who looked to have made the game safe by finding the top-left corner in wonderful fashion.
