The win lifted Inter to third in Serie A with 63 points, two ahead of AS Roma and Lazio who both play on Wednesday. The top four qualify for next season's Champions League group stage.
The only sour note for Inter was that midfielder Roberto Gagliardini pulled up clutching his thigh in the first half and was taken off on a stretcher with what appeared to be a serious injury.
In a move likely to shock traditionalists, Inter's shirts carried their players' social media handles instead of names to celebrate what the club described on Twitter as #InterSocialNight.
Joao Cancelo got Inter off to a flying start by scoring from a free kick which evaded everyone in the penalty area and landed in the net after three minutes.
Inter missed a host of chances before Mauro Icardi fired in from Rafinha's layoff four minutes after halftime, the Argentine's 25th league goal of the season.
Marcelo Brozovic curled in the third on the hour and Ivan Perisic blasted the fourth in the last minute.
Cagliari, who barely threatened, are 14th with 32 points, five clear of the relegation zone.
(Writing by Brian Homewood in Bern; Editing by Toby Davis)
