Chasing 128 runs, Uttar Pradesh required 16 runs off the last over with just two wickets in hand.
Imtiyaz Ahmad (15 not out) struck two sixes in the last over to take his side home.
Uttar Pradesh's middle-order batsmen made useful contributions with Mohd Kaif and Tanmay Srivastava scoring 24 each and sharing a crucial 44-run stand for the third wicket after their side was reduced to 20 for two in the fifth over.
Earlier, Baroda scored 128 for eight with H H Pandya top-scoring with an unbeaten 37. Pandya shared a 48-run stand with J B Chhaya (22) for the fourth wicket to provide some semblance of respectability to the score.
More From This Section
For UP, A S Mishra was the most successful bowler with figures of three for 23 while Imtiyaz took two for 20.
Meanwhile, a good all-round performance helped Kerala register a comfortable six-wicket victory over Odisha after they were dismissed for a modest 125 in a Group A encounter.
For Odisha, opener Ankit Yadav made run-a-ball 28 which included three fours.
A 35-run partnership for the ninth wicket between Lagnajit Samal (20) and Suryakant Pradhan (18) took Odisha past the three digit mark.
Pacers Nizar Niyas (2/24) and VA Jagadeesh (2/10) bagged two wickets each while left-arm spinner Padmanabhan Prasanth got one wicket.
Kerala, in reply, were 44 for three in 7.5 overs.
Sanju Viswanadh scored unbeaten 41 runs including two sixes and a four, and shared a 64-run stand with Sachin Baby (33) to take Kerala home.