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.
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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).