Chasing, 132 to win, Baroda were staring an unexpected defeat after being reduced to 108 for nine but Patel and Bhatt stitched an unbeaten 25-run partnership to steer the side home at Bansi Lal Cricket Stadium.
It meant that Haryana fast bowler Mohit Sharma's sensational five-wicket haul went in vain and Baroda walked away with six points.
The bowlers dominated the fourth and final day of the match as in all, 17 wickets fell.
The hosts began their second innings at a comfortable 127 for two but lost the remaining eight wickets with the addition of just 33 runs with Bhargav, Murtuja Vahora and Gagandeep Singh sharing the spoils. They took three wickets each.
Baroda would have hoped an easy cakewalk while chasing a modest 132-run target but Mohit Sharma bowled their opener Kedar Devdhar in the very first ball to begin the Haryana defense in style.
It got worse from bad for Baroda as soon they were struggling 33 for five. A 37-run stand for the seventh wicket between Saurabh Wakaskar (22) and Gagandeep Singh (24) revived their hopes but run out of the former again turned the tide in favour of Haryana.
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Mohit bowled Ganagdeep too and also Haryana skipper Amit Mishra scalped Vahora (12) to bring the side close to win.
However, Utraksh and Bhargav showed nerves of steel to cross the finish line.
Brief Scores:
Haryana 295 and 160 in 74 overs. (Sunny Singh 57, Abhimanyu Khod 38; Murtuja Vahora 3/31).
Baroda 324 and 133 for 9 in 33.5 overs.(Gagandeep Singh 24; Mohit Sharma 5/50).