Opting to bat first, Leicestershire were gasping for breath at 63 for five before Jeremy Snape (38 off 30 balls) and John Sadler (33 off 26 balls) steadied the ship as the side reached 136 for eight in the stipulated 20 overs.
Mongia began promisingly and struck three boundaries before Charlie Shreck removed him after a 21-ball knock of 17.
Chasing a victory target of 137, Nottinghamshire took 18.1 overs to reach the score losing five wickets.
Mark Ealham stole the thunder with his unbeaten 31 which came off just seven balls and he blasted four sixes in his explosive innings, while David Hussey was not out on 44 off 36 deliveries.
Mongia ended with a bowling figure of 1.1-0-5-1 with Chris Read as his victim.