Antonio Conte's Inter looked to be bringing home maximum points from his hometown team, where he started his footballing career in the 1980s, when Alessandro Bastoni headed the away side in front with 18 minutes remaining.
But Marco Mancosu grabbed a precious point for the southerners five minutes after going behind.
Inter have won just two of their last six league games but are one point behind leaders Juventus, who can however open up a four-point advantage when they host Parma later on Sunday.
Conte's side are now also under threat from Lazio who are just two points behind with a game in hand after hammering Sampdoria 5-1 on Saturday.
Cagliari extended their winless run with a 2-2 draw at relegation-threatened Brescia with Ernesto Torregrossa bagged a brace for the hosts.
The sixth-placed Sardinians have not won in the league since December 8.