Gurkeerat Maan (70 not out) was rock solid from one end but the visitors are still 393 runs behind as paceman Pankaj Singh took three wickets for 56 runs.
Rajasthan piled up 433 runs after resuming the day 295 for four. Pranay Sharma, who was unbeaten on 118 could not continue for long and departed after scoring 140 runs off 318 balls. He hit 19 boundaries and one six.
For Punjab leg-break bowler Sarabjit Ladda was the most successful bowler claiming four for 104 while Sandeep Sharma took three for 106. Sunny Kaul, Baltej Singh and Amitoz Singh took a wicket each.
Chasing a big total, Punjab were soon in trouble as Deepak Chahar, Pankaj Singh and Aniket Choudhary struck in quick succession to reduce the visitors to 40 for 3 at tea.
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Yuvraj Singh (3), whose hopes of inclusion in the Indian World cup team were dashed, fell just after the break and then Pankaj Singh struck twice to send visitors reeling at 140 for 5 at the close.
For Rajasthan Deepak Chahar and Aniket Choudhary grabbed a wicket each.