Chasing a modest target of 179, Abahani lost opener Jishan Alam early for just six runs. However, Shanto took control of the innings and ensured there were no further problems for his side.
Shanto remained unbeaten on 108 off 90 balls, leading the chase with an impressive knock, while Mahidul Islam Ankon provided strong support with an unbeaten 56 from 86 deliveries.
The pair shared a match-winning 171-run partnership as Abahani comfortably reached the target.
Earlier, Agrani Bank elected to bat first after winning the toss but were bowled out for 178 in 43 overs. Nasir Hossain top-scored with 56 off 58 balls, while Imrul Kayes contributed 30 runs.
Abahani’s bowling effort was shared among several players, with Rohan Ud Doula, Rakibul Hasan, Khaled Ahmed, Mosaddek Hossain and Mahfuzur Rabbi each picked up two wickets.
The win moved Abahani to second place in the points table with five victories from seven matches, behind Mohammedan Sporting Club, while Prime Bank Cricket Club sit third.