The striker struck just past the hour mark to cancel out Carlos Tevez's fifth minute opener and inadvertently help out their Serie A rivals at the top of the division
Carlos Tevez opened the scoring after just five minutes but Icardi struck shortly after the hour mark to seal a point, with the away side holding on following Mateo Kovacic's late red card.
The result means second-placed Roma are now just a single point behind leaders Juventus, with both sides having played 17 games.
Juve showed no signs of their recent blip in the early stages, putting Inter under pressure right from the start and they almost went ahead in the second minute, with Fernando Llorente slicing just wide from 14 yards.
Inter failed to heed that warning, though, and Juve duly broke the deadlock just three minutes later.
Vidal flicked the ball past his Chile team-mate Gary Medel with an exquisite first touch inside the area, before sliding an inviting pass into the goalmouth for Tevez to steer home.
The goal appeared to spark Inter into life as the visitors started to dictate proceedings, though the champions never looked particularly worried at the back and remained a serious threat on the break.
And, unsurprisingly, Juve's next opportunity came at the end of a swift counterattack, as Samir Handanovic was forced to push a Vidal drive around the post.
Handanovic was at the centre of things again nine minutes before the break, blocking a Pogba effort from close range after the Frenchman delightfully slalomed between Juan Jesus and Andrea Ranocchia.
Mancini looked to give Inter extra attacking impetus by introducing Podolski for his debut eight minutes into the second half, though the German struggled to make an impact from the left.
Juve continued to look threatening on the break and they were unlucky not to get a penalty in the 58th minute as Juan clumsily tripped Llorente.
Inter capitalised on that let-off, though, with Icardi beating Gianluigi Buffon from a tight angle after beating Giorgio Chiellini to Fredy Guarin's through ball.
The Argentina striker then agonisingly missed the target from point-blank range following Podolski's cross with nine minutes to go.
However, Kovacic's late red card for a crude challenge on Stephan Lichtsteiner effectively ended their chances of victory, with Patrice Evra seeing a deflected shot saved by Handanovic as the game ended 1-1.