After being bowled out for 135 in their first innings that gave Railways a substantial lead, the visitors were 153 for two at the close of play on the third day.
At stumps, Robin Bist (35) and Ashok Maneria (29) were at the crease.
Ahead of a gruelling final day's play, Rajasthan trailed Railways by 117 runs with eight wickets remaining.
Resuming on 56 for three in response to the hosts' first-innings total of 405, Rajasthan lost wickets at regular intervals to lend Railways the upper hand.
Anureet finished with figures of five for 40 from his 24 overs, while his other pace colleague, Ranjitkumar Mali, picked up three wickets for 42 runs. Skipper Sanjay Bangar also chipped in with two wickets.
The start was disastrous for Rajasthan as they lost skipper Vineet Saxena (22) for the addition of just six runs to the team's overnight total. Rashmi Ranjan Parida too departed for eight as Rajasthan slumped to 76 for five.
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Maneria, who was looking good at the other end, failed to convert a good start into big score as he fell for 27 to Mali.
With 162 still needed to make the hosts bat again, Rajasthan's batting looked in complete disarray with the Railways seamers, led by Anureet, exploiting the conditions by bowling an accurate line and length.
Anureet further compounded the misery for Rajasthan when he had Gajendra (13) and Manjeet Singh (0) in his same over.
Aniket Choudhury and Sumit Mathur, too, departed soon as Railways put themselves in the driving seat.
Following-on, Rajasthan responded strongly in their second innings with Sourabh Chauhan hitting a fine half century and together in the company of Saxena stitched a 76-run stand for the opening wicket.
While Chauhan fell to Mali caught by Mahesh Rawat, Saxena was trapped in front of the stumps by Karan Sharma.