The diminutive Patel kept the one end tight but did not get support from his batting colleagues after being invited to bat at Dr DY Patil Sports Academy ground.
India's struggling paceman Zaheer Khan also had a decent day as he bowled 17 overs and took two wickets for 40 runs.
Left-arm spinner Ankeet Chavan (3/54) was the most successful bowler for Gujarat with three wickets while Javed Khan (2/46) took two.
However, Gujarat began the defence of the total by taking an early wicket in opener Kaustubh Pawar, who scored 17 before being caught of Chirag Gandhi off Rakesh Dhruv. With Pawar's dismissal, stumps were drawn for the day.
Mumbai ended the day at 24 for one with Wasim Jaffer (6) on strike.
Apart from Patel only three other Gujarat batsmen reached the double-digit score with Bhargav Merai being the second best scorer with his 41-run knock.
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Patel came to the crease after Gujarat had lost both the openers Smit Patel (8) and Samit Gohel (30) and was the second-last man out.
Left-hander Patel's 101 came off 146 balls and his knock had 12 boundaries in it.
Brief Scores:
Gujarat 1st innings: 244 all out in 78.3 overs. (Parthiv Patel 101, Bhargav Merai 41; A Chavan 3/54, Z Khan 2/40)
Mumbai 1st innings 24 for one in 8.3 overs. (Kaustubh Pawar 17; R Dhriv 1/5).