Menaria (150 not out) was helped by his team-mates Rajat Bhatia (64) and Dishant Yagnik (58 not out) in Rajasthan's effort to draw the Group B match and at least secure one point out of the tie at the Sawai Mansingh Stadium.
Maharashtra got three points on the basis of their 91-run first innings lead.
Rajasthan, who began the day precariously placed on 115 for 3, were driven by a 127-run fourth-wicket stand between Menaria and Bhatia.
Bhatia, making his Rajasthan debut, finished with scores of 59 and 64 in two innings.
With the game all but secured, Menaria found support from Yagnik as the two shared an unbroken 149-run stand to puncture Maharashtra's hopes.
Set a target of 244 for a win, the visitors' chase was merely a formality. They scored 17 without loss when the match ended in a draw.
Maharashtra 409 (Rahul Tripathi 119, Chirag Khurana 77; Ankush Bikram Singh 4/87, Chahar 3/94) and 17 for 0 drew with Rajasthan 318 (Ashok Menaria 84, Rajat Bhatia 59; Samad Fallah 3/77, Shrikant Mundhe 3/94) and 334 for 5 dec (Ashok Menaria 150 not out, Bhatia 64; Mundhe 2/51).
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