Following on, Rajasthan were 13 for no loss in their second innings at stumps on the third day.
For Saurashtra, Jaydev Unadkat, Shaurya Sanandia and Dharmendrasinh Jadeja picked up three wickets each at the Sawai Mansingh Stadium.
Resuming at their overnight score of 60 for two, Rajasthan lost the day's first wicket when opener Chetan Bist (41) was trapped in front by Unadkat with the scorecard reading 83.
Robin Bist, who top-scored in Rajasthan's first innings with 63 off 148 balls, added 99 runs for the fourth wicket with Ashok Menaria (46).
These efforts were not enough for Rajasthan as they struggled to go close to the visitors' massive first-innings total of 534 all out.
When the stumps were drawn on the penultimate day, the hosts trailed by 246 runs, albeit with all second innings intact.