Mongia had slammed an unbeaten 129 off 234 balls, including 18 boundaries, in the first innings as the hosts declared their first innings at 315 for nine.
In reply, Pakistan declared their first innings at 304 for five with Salman Butt (68), Imran Farhat (81) and Kamran Akmal (62) struck half centuries.
In their second essay, Leicestershire were in trouble with Pakistani pace duo of Mohammad Sami and Umer Gul looking ominous, while leggie Danish Kaneria also claimed two wickets and looked hungry for more.
Leicestershire relied heavily on Mongia but the Punjab southpaw fell victim to law of average despite an early flourish. He had hit two boundaries and looked aggressive before perishing caught behind off Shahid Afridi for just 14 that came off eight deliveries.