The Nerazzurri were on top for most of the encounter but were forced to dig deep for victory as the Serbians proved to be stubborn opponents
Rodrigo Palacio was the eventual hero after he came off the bench to net the all-important winner, but not before the visitors came within a fraction of recording a shock victory.
Coutinho was arguably Inter's most dangerous player in the opening stages, looking to break clear of the Serbians' defence on any given occasion, but he was guilty of missing the game's first clear-cut opportunity.
It came on nine minutes as Jonathan's cross-field pass was brought down by Alvaro Pereira, but the Brazilian could not finish off the left-back's cross with the goal at his mercy. His night was soon cut short due to an ankle knock and he was duly replaced by Palacio.
But that did not deter the visitors from making a positive start at the Giuseppe Meazza and Lazar Markovic did wonderfully well, coming in from the left, to show Jonathan a clean set of heels and curl a strike onto the post.
Their fearless approach was almost rewarded for a second time as Matias Silvestre appeared to have conceded a penalty following a cynical challenge on Aleksandar Mitrovic. However, the infringement was deemed to have been outside the box and Nemanja Tomic could only hit the side-netting with the resulting free kick.
But despite such a promising opening, the action turned into a dour affair after the half-hour mark as both sides drifted into a lull. A string of fouls followed, with three yellow cards being shown to guilty offenders in the final 15 minutes of the opening period.
Fans who were expecting an improvement after the break were to be disappointed. A scrap ensued for most of the second half; Partizan, bottom of Group H on goal difference before the fixture, were only too happy to settle for a point.
Antonio Cassano then squandered a golden chance to claim victory midway through the second half. The Italy star was on the receiving end of a cross from Palacio, but he inexplicably ballooned his effort over the bar despite being in bundles of space in the box.
Inter remained on top for what was left of the encounter, but without ever truly threatening. Coach Andrea Stramaccioni threw on Diego Milito in a bid to salvage a winning goal, and although the Argentine did come close via a snapshot, even he could not find the back of the net.
And when Markovic, through on goal, came within a whisker of beating Handanovic with not long left, it was enough of a warning sign for the former European champions to spark into life and find the winner. Palacio popped up in the box to freely head in for the three points.
The last-gasp victory puts the Italians level with Rubin Kazan, who beat Neftchi Baku 1-0 earlier on Thursday, at the top of Group H.