Mongia's 129, which came off 234 balls, had 18 boundaries in it and he remained at the crease for five hours and 10 minutes.
The batsman from Punjab shared a valuable 174-run fourth wicket stand with Jon Sadler (92), besides another 58-run partnership with opener Darren Robinson (34).
After being inserted by Younis Khan, who led the visiting side, the Foxes began on a disastrous note, with debutant Matthew Boyce falling for four and HD Ackerman lasting only four deliveries for a duck.
For the visitors, Mohammad Sami defied a slow pitch to capture three for 53 in his 17 overs while Umar Gul snared two Leicestershire batsmen.
Salman Butt and Imran Farhat then began a watchful reply as Pakistan reached 14 without loss at the draw of stumps.
Pakistan rested captain Inzamam-ul-Haq, batsman Mohammad Yousuf, all-rounder Abdul Razzaq and fast bowler Mohammad Asif.
Brief scoreboard: (Leicestershire 1st innings: 315 for nine declared; Dinesh Mongia 129 not out, Jon Sadler 92; Darren Robinson 34; Mohammad Sami 3 for 53; Umar Gul 2 for 52) Pakistan 1st innings: 14 wothout loss; Salman Butt 7 not out; Imran Farhat 7 not out)