Resuming at 290 for three, skipper Patel and Y Venugopal Rao (95) kept the Punjab bowlers at bay, raising a 188-run stand for the fourth wicket.
Venugopal Rao missed out on his hundred when he was stumped off Jiwanjot Singh.
Once that stand was broken, Punjab bowlers took wickets in heap as Gujarat lost last six wickets for just 58 runs.
Patel's 113 came off 190 balls with 10 shots to the fence while Venugopal took 187 balls to score 95 which had 12 boundaries.
Punjab came out to bat and the openers -- Manan Vohra (50 batting) and Jiwanjot (51) provided a great start by raising 83 runs for the first wicket.
Jiwanjot was dismissed by off-spinner Ruzul Bhatt and then Uday Kaul (24 batting) stayed at the crease till stumps with Vohra, ensuring that the hosts do not lose any more wicket on day 2.