Gupta scored 144 runs off 240 balls as UP declared their second innings at 319 for five after beginning the day at 46 for two at Sawai Mansingh Stadium.
Gupta's overnight partner and skipper Mohammed Kaif (19) could add only 15 runs to his total but Arish Alam (42) and Parvinder Singh (50 not out) batted well with him.
Paceman Aniket Choudhary (48) took all the three wickets that fell in the day.
Gupta's knock came off 240 balls and he struck 21 fours and two sixes before being caught behind.
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Brief Scores:
Uttar Pradesh 226 and 319/5d (Prashant Gupta 144, Parvinder Singh 50 not out ; Aniket Choudhary 3/48).
Rajasthan 185 and 15 for no loss in 4 overs.