Argentine Matias Defederico scored the match-clincher in the 69th minute at the Shree Shiv Chhatrapati Sports Complex.
Pune were without their new coach, the suspended Antonio Habas, who will sit out Pune's first four matches after being sanctioned for indecent behaviour last year, when he was helming Atletico de Kolkata.
The home team were the enforcer in the early exchanges of the match. They received two free-kicks in promising positions but shot them straight into the defensive wall to squander the opportunities.
Moments later, Pune's midfielder Jonatan Lucca's left-footed volley was acrobatically saved by Mumbai goalkeeper Roberto Volpato, diving to his right in the 15th minute. Pune forward Gustavo Oberman then threatened from the right flank a minute later.
Mumbai's marquee player Diego Forlan couldn't involve himself with the flow of the match.
The Uruguayan seemed off pace and struggled to combine with his team-mates as Mumbai struggled to create any meaningful opening.
After Pune's initial thrust the action lacked rhythm as it was apparent that both teams were playing their first competitive matches of the tournament.
Oberman was comparitively prominent, entering Mumbai's penalty box menacingly from the left channel in the 42nd minute.
He synced his run with a through pass perfectly and was one-on-one with Volpato. But the onrushing goalkeeper smothered Oberman's attempt to place the ball past him.
Mumbai finished the half stronger with Forlan engaging in a one-two pass with defender Lalhmangaihsanga Ralte.
Forlan's left footed pass for Brazilian Leo Costa was accurate but the midfielder's shot was blocked by Pune defender Gouramangi Singh.
The lack of flow in the proceedings didn't change even after the break as too may stoppages hindered swiftness.
The match needed a moment of inspiration to be lifted from mediocrity.
Devoid of service, Forlan dropped deeper into the midfield zone, to get more involved with the proceedings.
He has a part to play in the goal that Mumbai score in the 69th minute, flicking it to the Argentine Defederico.
Defederico's controlled left-footed grounder shot beat Pune's scampering goalkeeper Edel Bete.
Pune could equalised five minutes later had Jonatan Lucca's pass to Spanish forward Jesus Tato not beaten away by Volpato at the near post.
Pune players moved up looking for the equaliser. Tato remained their most likely source for a goal as his shot in the 81st minute was again thwarted by Volpato.