Abbas, who hit 17 fours in his 202-ball unbeaten knock, stitched a 110-run partnerships with Udit Patel (49) for the third wicket from 40.2 overs as Tripura ended the day on 285 for four from 106 overs after resuming at 53 for no loss today at Maharaja Bir Bikram College Stadium.
The home side were still trailing by 278 runs with six first innings wickets in hand and one day still to go. Services had made a massive 563 for four declared in their first innings.
If Tripura continue today's fine batting display tomorrow without being all out and their total less than that of Services, both sides will end the Group C match on one point each.
Earlier in the morning, openers Subhrajit Roy (64) and Samrat Singha (38) added another 48 runs to their overnight 53 before the latter was out in 39.2 overs after sharing 101 runs to give a strong start to the home side reply.
At stumps, Abhijit Dey was giving company to Abbas Ali on eight.
For Services, Shadab Nazar took two wickets for 70 runs while Suraj Yadav and Yashpal Singh grabbed a wicket each.
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Brief Scores:
Services 1st Innings: 563/4 declared
Tripura 1st Innings: 285 for four in 106 overs (Abbas Ali 108 batting, Subhrajit Roy 64; Shadab Nazar 2/70).