Put into bat, Leicestershire were all out for 371 in their first essay and Mongia's contribution with the bat was a mere seven.
In reply, Gloucestershire scored 282 for nine in their second innings and Mongia claimed a wicket conceding 23 runs in his nine overs.
Back up against wall, Leicestershire put up a poor show in their second innings and were all out for 233 in 76.3 overs.
Mongia was the highest scorer in the second innings, hitting a 93-ball knock of 62 that included 11 hits to the fence before Jon Lewis castled him.
Chasing a victory target of 323, Gloucestershire reached the score losing just three wickets with Alex Gidman hitting an unbeaten 115.
Mongia went wicketless in the second innings and gave away 23 runs in his eight overs.