Keita Manjdou (62nd) and Gurjinder Kumar (84th) scored for the visitors.
Earlier, both the teams fought on an even note in the barrren first half as the hosts made clear their intention to extend their lead on top of the table through an aggressive display.
Lanrindika Ralte came up with a fierce shot from the top of the box only to see his shot hitting the bar in the second minute. Five minutes later rival custodian Abhara Mondal had to come and thwart Henri Autchouet from scoring off a cross from Lalrindika.
Mondal came to his side's rescue again when he blocked the ball off a freekick taken by Roberto Silva.
The visitors slowly settled into the groove and launched a series of moves and had three clear chances to surge ahead but Karma Tsewang failed to find the mark from close and later defender Chika Wali failed to convert twice.
After the change of ends, Churchill Brothers were unlucky when Lalrindika's shot hit the bar off a long pass from Denzil Franco from the right.
Thereafter, the momentum shifted in favour of visitors who controlled the midfield and kept on having better ball possession and took the lead in the 62nd minute.
A quick build up on the right which saw Srikant Ramu send a measured cross into the rival box which defender Naveen Sudhakaran allowed to get past. Striker Keita Manjdou, who was following the move, met the ball with a glancing header to find the back of the net.
Lester Fernandes, who played a dominant role in the midfield, played a one-to-one pass with Keita Manjdou on top of the box and the former, on entering box, took a shot which Churchill's keeper Felix D'Souza managed to block.
Pune FC made the issue safe when they scored again in the 84th minutes to seal Churchill Brothers' fate of any comeback.
Following a build up in the middle, Keita Manjdou took a crack at the goal from inside the box but Churchill custodian Felix, who left his charge, managed to block the shot.
However, defender Gurjinder Kumar found the net with a stiff grounder off the rebound.
The win takes Pune FC to fifth place with 18 points from 11 matches.
Churchill Brothers remained on 23 points from as many matches. Dempo, who are two points behind them, have a good chance to regain the top spot if they beat Sporting Clube de Goa on Thursday.