Chasing 431 for victory, Gujarat's one-down batsman Bhargav Merai chipped in with a crucial 54, while Manpreet Juneja (91 off 101 balls) and Axar Patel (80 off 89) played gritty late-order knocks, adding 142 runs off 153 balls for the seventh wicket, but failed to avoid defeat.
Saurabh, who claimed five for 37 in the first innings, once again wreaked havoc by taking five for 106 in the second essay to give the visitors an outright win.
Chasing a massive target, Gujarat lost two early wickets to be reeling at 6 for two inside five overs.
The home team, however, steadied the boat with a 60-run stand between Merai and captain Parthiv Patel (18).
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But after Praveen Kumar dismissed Parthiv, Gujarat suddenly found themselves reduced to 110 for six from 66 for three with left-arm spinner Ali Murtaza (3/38) picking up two of the three wickets to fall.
Saurabh finished with a match haul of 10 for 143.
Brief scores:
Uttar Pradesh: 273 & 257 (Piyush Chawla not out 62, Axar Patel 5/90).
Gujarat: 100 & 275 (Manpreet Juneja 91, Axar Patel 80; Saurabh Kumar 5/106, Ali Murtaza 3/38).
Points: UP 6, Gujarat 0.