The result was the host' best-ever over their Kolkata rivals in 11 meetings and also stretched their unbeaten run in this season's league to seven.
The architect of the victory was striker James Moga (8th and 77th minute) and defender Othallo Tabia (17th).
Striker C K Vineeth (51st) pulled one back for the visitors to cut back the lead and give them some hope after the breather.
After this win, Pune FC moved up to third place with 23 points, while Prayag stayed at fifth place with 17 points. The victory was also Pune FC's third at home.
