Ajay Jadeja with 49 and Mohd Aslam with four runs were at the crease when stumps were drawn for the day. Rajasthan still require 64 runs to make Mumbai bat again.
For Mumbai, getting five points including a bonus is a must if they want to have a chance of qualifying for the semifinals. They will get five points if they win by an innings or by 10 wickets.
Earlier, starting the day at 464 for eight, Mumbai stretched their innings to 483 before being bowled out 28 minutes into the day.
Rajasthan, needing to score a minimum of 328 runs to make Mumbai bat again started disastrously when first innings saviour Vikram Solanki was dismissed for zero edging a perfect outswinger from Ajit Agarkar to the keeper with Rajasthan on nine.
Mumbai should have accounted for Gagan Khoda when he was on eight and the score on 15 but Hiken Shah dropped a regulation third slip catch with Agarkar being the loser. In the next over, Agarkar again missed out on a wicket when Swapnil Hazare dropped R Kanwat at fine leg with the batsman on 2.
The two then made Mumbai pay as they took the bowlers to the cleaners with superb attacking strokeplay. Gagan Khoda was especially severe on off spinner Ramesh Powar hitting him for two huge sixes to reach his 50 in just 64 balls with nine fours and two sixes.
However, soon after lunch Khoda fell to Nilesh Kulkarni trapped leg before as he missed a sweep and the ball struck him plumb in front of the wicket. Khoda made 65 studded with 11 boundaries and two sixes.
Kanwat was the next to fall after reaching his 50 being caught behind by Vinayak Samant of off spinner Ramesh Powar for 60 to leave Rajasthan on 138 for three.
Mumbai, then sensing victory stepped on the pressure to reduce Rajasthan to 242 for seven, before captain Ajay Jadeja with an unbeaten 49 saw the day through with spinner Mohd Aslam.