The left-hander's unbeaten 142 took the home side to 303 at stumps. Mongia received good support from John Maunders (71) and John Sadler, 47 not out at the close.
In the top flight reigning champions Nottinghamshire bowled Sussex out for just 143 at Hove.
Nottinghamshire's only four-day victory of the season so far was against MCC but they bounced back from defeat by Warwickshire to make Sussex captain Chris Adams regret his decision to bat first.
Former England seamer Mark Ealham led the Nottinghamshire attack with two wickets for 17 runs while Ryan Sidebottom, Graeme Swann and Paul Franks also picked up two victims each.
And Australian batsman David Hussey also took a wicket with his solitary over of off-spin.
Nottinghamshire finished the day on 72 for two, Russell Warren and Hussey the men out and stand-in skipper Jason Gallian retired hurt.
Hampshire, the 2005 runners-up, saw opener Michael Carberry score a hundred away to Warwickshire at Edgbaston.
Carberry's 102 took 170 balls and he shared an opening stand of 113 with James Adams, the latter leg-before to Neil Carter. Alex Loudon dismissed Carberry before also getting rid of Zimbabwean Sean Ervine.
Former England batsman John Crawley will start the second day on 65 not out with Hampshire 280 for four after Australian Dominic Thornely (42) fell just before the close.