Rajasthan saved the match, ending the final day at 236 for seven in their second innings in a chase of 405.
Saxena and Bist resumed the hosts innings and added 106 runs for the second wicket. Both of them were scalped by left-arm Ravikumar Thakur, who had them caught behind.
Saxena faced 182 balls and hit nine boundaries in his patient knock while Bist's innings came off 139 balls with nine shots to the fence.
Thakur (3/54) was the most successful bowler for Vidarbha with three wickets while Swapnil Bandiwar (2/31) and Rakesh Dhruv (2/81) took two wickets apiece.
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Brief Scores:
Vidarbha: 296 and 296 for 4 declared
Rajasthan: 188 and 236 for seven in 102 overs.(V Saxena 52, R Bist 54; R Thakur 3/54, S Bandiwar 2/31).