The Indian started fourth on the grid and worked his way up the ladder, but failed to hold on to the challenge from Hare who began at third. Fellow Indian Akhil Khushlani finished seventh, while Raj Bharath and Vishnu Prasad ended ninth and 10th respectively.
Championship leader Nabil Jeffri started on pole but slipped down the order after being handed a drive-through penalty for a false-start infringement. Saturday's race winner Afiq Ikhwan, who began in second position, finished fourth.
"It's a great feeling being on the podium here in front of my home crowd," said Patel, who is the US Formula Project driver.
King of the jungle
Jordan King made an emphatic return to the top step of the podium in Race 2 of The MRF Challenge. Starting again from pole position, he once more got out-dragged into the first corner, this time by Jon Lancaster.
Jordan fought back hard and after a battle that lasted a few laps, managed to pull off an impressive overtaking manoeuvre. From then on, he was the leader for the rest of the race.