With the scores level, Rana removed Janat, who hit three fours and two sixes in his brief stay.
New batsman Mohammad Wasim hit the very first ball for a four to take the team home. Salman remained unbeaten on 18 runs in 14 balls with the help of two fours and a six.
Earlier, Barisal fast bowlers Khalid Ahmed and Kamrul Islam took two wickets each while pacer Mohammad Wasim took 1-22 in four overs to strangle Chattogram’s innings.
However, Afif Hossain’s 23-ball 37 and Curtis Campher’s unbeaten 25-ball 45 helped Chattogram post a challenging total.
After the win, the Shakib-led side now have 12 points from eight matches.
Mashrafe Bin Mortaza-led Sylhet Strikers also have the same number of points but have slipped to second place on net run rate for the first time after their six-wicket loss to Rangpur on Friday.