Bengal declared their first innings at overnight score of 528 for eight at the start of the day and the hosts batted with resolve, ending the day at 296 for three.
They are still trailing by 232 runs and have a task at hand to avoid conceding first innings lead.
Bengal paceman Ashoke Dinda removed Harshad Khadiwale (5) in the fifth over of the day but Swapnil Gugale (35) and Sangram Atitkar (69) added 56 runs for the second wicket.
Dinda dismissed Atitkar but Tripathi continued to bat impressively in the company of Bawne. The hosts did not lose any wicket in the final session of the day.
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Tripathi has hit 13 fours and two sixes in his 227-ball knock so far.
Brief Scores:
Bengal 1st innings: 528/8d
Maharashtra 1st innings: 296 for 3 in 90 overs.(R Tripathi 116 batting, S Atitkar 69; A Dinda 2/77).