Mumbai needed four runs in the final over to achieve a 146-run target, but seamer Patel conceded just one to boost Rajasthan´s chances of making it to the semi-finals.
Three wickets fell in the last over, including two run-outs.
Skipper Sachin Tendulkar hit a solid 40 off 30 deliveries and Abhishek Nayar an 18-ball 35 to raise Mumbai´s hopes of victory following man-of-the-match Shane Warne´s triple-strike, but Rajasthan hit back in the closing over.
Former Australian leg-spinner Warne finished with 3-24.
Mumbai´s hopes rested on Tendulkar and Sanath Jayasuriya (16), specialist openers batting in the middle order, after three wickets had fallen for 23 runs but skipper Warne removed both the batsmen at the right time.
Delhi lead the eight-team tournament with 16 points from 10 matches, followed by Chennai (13/11), Rajasthan (13/12), Deccan (12/11), Bangalore (12/12), Mumbai (11/12), Punjab (10/11) and Kolkata (3/11).
The top four sides advance to the semi-finals.
Australian opener Rob Quiney and Indian middle-order batsman Ravinder Jadeja earlier boosted Rajasthan with a 61-run stand for the third wicket off just six overs.
Quiney top-scored with a 40-ball 51 for his maiden half-century of the tournament, while Jadeja scored 42 off 32 balls.
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