Services, at 154 for five, were leading by 20 runs when the day ended.
Sent into bat, Services suffered an early setback when opener Mukul Dagar (5) was dismissed by medium-pace bowler Nishan Singh.
UP skipper Mohammad Kaif (6) followed soon as he was trapped in front of the wicket by Nishan for his second wicket.
The following batsmen -- Eklavya Dwivedi (1) and Parvinder Singh (1) too, failed to to contribute. Left-handed opener Tanmay Srivastava scored 20 off 71 balls.
Reduced to 40 for five at one stage, Piyush Chawla scored a quick 28, with the help of four fours and a six.
A flurry of runs from pacer Imtiaz Ahmed towards the end helped Services cross the three-figure mark. His blazing half-century (53) came off just 35 balls and comprised four sixes and three fours.
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For Services, medium pacer Shadab Nazar ended up with an impressive figures of five for 51 in 13 overs. New ball bowlers Suraj Yadav and Nishan Singh bagged two and three wickets respectively.
The Services batsmen, in reply, failed to capitalise on their starts with openers Nakul Verma (27) and Ansuhl Gupta (26) being dismissed with 67 runs on the board.
They were reduced to 97 for five, before right-hander Rajat Paliwal and wicketkeeper Sarabjit Singh got together at the crease and shared an unbeaten partnership of 57 runs to take Services past UP's first-innings score.
Rajat was batting on 36 and Sarabjit on 31 at the close of play.
UP seamer Imtiaz Ahmed was among the wickets as well as he got three wickets for 54 runs. Pacer Sudeep Tyagi got two for his team.