Icardi had netted on his previous three visits to Cagliari and again savoured his love affair with the Sardinian capital as he became the league's joint top scorer, taking his season's tally to 15, level with Lazio's Ciro Immobile.
The win put Inter on top of the standings with 36 points but Napoli, who have 35, can reclaim top spot when they visit Udinese on Sunday, while champions Juventus, third on 31, host Crotone.
Icardi opened the scoring against the run of play with a finish from close range in the 29th minute after Inter goalkeeper Samir Handanovic had already made three saves to keep the home side at bay.
Marcelo Brozovic struck a second in the 55th minute, moments after coming off the bench, and after Leonardo Pavoletti had pulled one back, Icardi sealed the win for Luciano Spalletti's unbeaten side with another close range finish in the 83rd.
It was the second week in a row that the Argentine striker had scored twice following the previous Sunday's double against Atalanta.
"The other teams know where we are, we're putting them under pressure and we will enjoy being top of the league tonight," said Icardi.
"This was the performance of a strong side, because we had some difficulties at the start," Spalletti added.
"We struggled to build moves from the back as Cagliari were pressing us so violently. Cagliari had an excellent start and we coped under pressure, the way a great team ought to."
Elsewhere, Hellas Verona, struggling in 19th place, snapped a five-game losing streak to win 2-0 at troubled Sassuolo despite playing the final 20 minutes with 10 players after Thomas Heurtaux was sent off for two yellow card offences.
"Unfortunately, the same things keep happening and our problem is a lack of character," Sassuolo's embattled coach Cristian Bucchi said, increasingly frustrated with his side's plight two points above the relegation zone in 16th place.
"We always start games well, but the moment the first difficulty arrives, the team loses its way. A coach can teach tactics and fitness, but not character."
Bologna eased to a 3-0 win at home to Sampdoria despite a red card for Vasilis Torosidis, who was booked twice inside a minute at the end of the first half.
Chievo Verona staged a second half comeback to beat SPAL 2-1 thanks to a double from Roberto Inglese.
(Reporting by Richard Martin; Editing by Ian Chadband)
