Barishal captain Tamim Iqbal won the toss and sent Rajshahi to bat first at Sher-e-Bangla National Cricket Stadium.
However, Rajshahi managed to put only 132 for nine on the board in 20 overs.
And Barishal chased the target of 133 runs, losing five wickets, in 19 overs, riding on Tamim's unbeaten knock of 77.
Earlier, Najmul Hossain Shanto and Anisul Islam Emon put up a stable opening stand of 39 runs in six overs, but they failed to hold onto the good momentum.
Najmul fell prey to Abu Jayed for 24 when Rajshahi were batting at 39 from 6.1 overs. Then, in the last ball of the next over, Mehidy Hasan Miraz removed Rony Talukdar for six.
Mohammad Ashraful came to the wicket at number three, playing an unbeaten 25 in the last game. But this time, he had to leave the field only for six, being caught short of the crease.
Also, Mehidy Hasan Miraz dismissed Anisul Islam Emon at 24 in the same over.
However, Fazle Mahmud (31) and Mahadi Hasan (34) responded well to help their team put up a fighting total.
For Barishal, Kamrul Islam Rabbi bagged four wickets, conceding 21 runs in four overs, while Mehidy took two and Abu Jayed and Taskin Ahmed scalped one wicket each.
In reply, Tamim remained unbeaten for 77 off 61 balls with 10 fours and two sixes to register his team's first win in the competition. Barishal ended up on 136 for five in 19 overs.
Tamim and Mehidy opened the innings for Barishal. While Tamim was firm in the wicket, Mehidy fell prey to Ebadat Hossain for one.
Also, Parvez Hossain Emon (23) and Towhid Hridoy (17) failed to accompany Tamim for a long time despite making good starts.
And the quick dismissals of Afif Hossain (0) and Irfaan Sukkur (3) made the going tough for Barishal. But Tamim finished off in style.
For Rajshahi, Mukidul Islam took two wickets while Ebadat Hossain and Mahadi Hasan bag one wicket each.
Also read: Bangabandhu T20 Cup: Rajshahi beat Khulna by 6 wickets