Striker Thongkhosiem Haokip (43rd minute) and winger Gabriel Fernandes (54th) scored for Pune.
The result completed Pune FC's first double-win over any team in the ongoing season and also ended their six-match winless run in all competitions since December.
At home, this was Pune FC's first win after four games which includes two losses and as many draws.
Pune FC's last win at home was on November 6 when they had beaten the league leaders Bengaluru FC 1-0.
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Fernandes was eager to take the match into Mohammedan forte but his ambitious run in the fifth minute on a pass from Anthony D'Souza was flagged offside.
Fernandes then collected a fine aerial shot from Douhou Pierre down the right wing, but Luciano Sabrosa cleared the attempt three minute later.
Pune FC had another chance in the 16th minute when Mustapha Riga controlled a long ball on the left and slid it back for Anthony, who crossed it for Haokip, but his header was blocked by the Mohammedan defender.
Then came the breakthrough. Defender Salam Ranjan Singh sent a long ball that saw Riga chasing down the right before lobbing it in front of goal where Haokip headed the ball home.
On changing the ends, Pune FC remained in relentless pursuit of openings. In the 53rd minute Riga gave a pass to Anthony on the left and he hit the ball from the edge of the box for Fernandes, who came running in and made no mistake to put it into the nettings.