Uniyal (4-69), Gagandeep Singh (3-88) ran through Baroda's second innings as the visitors, who set a target of 391, were bowled out for 280 on the fourth and final day. Punjab got four points from the win.
The hosts, who had taken a first innings lead of 20 runs, declared their second innings at the overnight score of 370 for four.
Rakesh Patel (69 not out), Satyajit Parab (49) and Jacob Martin (44) put up a semblance of fight but could not help Baroda reach anywhere near the target as the other batsmen failed to counter the hostile bowling by the Punjab seamers.
When Patel came to bat, Baroda were reeling at 172 for seven, but the tail-ender with the help of last two batsmen -- S Joshi (8) and Irfan Pathan (senior) (11) -- added 108 runs for the last two wickets to take the score past the 200-mark.