Pujara (115) and Patel (156) shared an unbeaten 252-run stand after new recruit Robin Uthappa fell in the 24th over.
It was good match practice for Pujara ahead of the Sri Lanka series that begins with the first Test at the Eden Gardens from November 16.
The gritty right-hander faced 188 balls and his effort included 15 fours. Pujara had broken Vijay Merchant's record of most double hundreds in first-class cricket by an Indian after scoring 204 against Jharkhand last week.
Brief scores: Saurashtra 311/1 in 90 overs (Pujara 115 batting, Patel 156 batting; Chawla 1/64).
At Rohtak: Haryana 99/7 in 44 overs against Rajasthan.
At Jamshedpur: J&K 355/6 in 90 overs (Khajuria 101, Bisht 101).