The Nerazzurri were on top for most part of the encounter but were forced to dig extremely deep for the win as the Serbians proved to be the most stubborn of opposition.
Rodrigo Palacio was his side's hero on the night, coming off the bench to net the all-important winning goal in northern Italy.
Coutinho was arguably Inter's most dangerous player in the opening stages, looking to break clear of the Serbians' defense 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. However, his night was cut short due to an ankle knock and he was soon replaced by Palacio.
That did not deter the visiting side 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 tackle on Aleksandar Mitrovic. However, the foul was deemed outside the box and Nemanja Tomic could only hit the side netting.
Despite such a promising opening, the action turned into a turgid 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 last 15 minutes of play.
Fans who were expecting an improvement after the break were to be disappointed. A scrap ensued for most part of the second half. Partizan, bottom of Group H on goal difference before the fixture, was only too happy to settle for the point.
Antonio Cassano then squandered a golden chance to claim the victory midway through the period. The Italy star was on the receiving end of a cross from Rodrigo 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 tie, 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.
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 champion to eventually find the winner. Palacio popped up in the box to freely head for the three points.
The last-gasp victory puts the Italians level with Rubin Kazan, which similarly beat Neftchi Baku 1-0 earlier in the evening, on top of the pool.
Follow GOAL.COM USA on