Mauricio Pinilla's penalty gave Cagliari a half-time lead but Inter equalised early in the second period, defender Rolando credited with the goal.
The result leaves fifth-placed Inter 10 points adrift of the top three, while Cagliari are five clear of the relegation zone in 15th.
Cagliari were quickly out of the blocks and Pinilla sent a bicycle kick over the bar before Victor Ibarbo fired a wayward effort high over.
Fredy Guarin's effort at the other end was also too high and Walter Samuel then headed Ricardo Alvarez's cross wide.
Inter went close in the 26th minute when Jonathan Moreira's cross was scrambled goalwards by Guarin but Luca Rossettini cleared with Diego Milito waiting to tap in.
Matias Vecino went close after a Cagliari counter-attack but their opener arrived five minutes before the interval when Jesus Juan's handball gave Pinillo the chance to score from the spot.
Walter Mazzarri's half-time talk, and introduction of Mauro Icardi in place of Milito, sparked Inter into life as the newcomer fired just over from Guarin's pass.
And Icardo was also involved in the 51st-minute equaliser. His shot may have crossed the line before Vlada Avramov parried it away, but Rolando followed up to make sure and was named as the goalscorer.
Guarin shot just over but Cagliari were by no means finished and Albin Ekdal and Ibarbo combined to set up Andrea Cossu, whose 20-yard shot flashed just wide.
Avramov made a good save from Rodrigo Palacio, following a neat one-two with the lively Guarin, to keep Cagliari level.
Sebastian Eriksson and Ekdal failed to threaten the Inter goal with long-range efforts and it was the hosts who had the better chances in the final quarter of the game.
But Avramov repelled Mateo Kovacic's dangerous free-kick and, in stoppage time, Guarin's long-range drive was blocked by Rossettini to ensure the game finished all square.