After this, Tamim and Mushfiqur Rahim led the team to victory with many balls remaining.
Mohammad Saifuddin (2-28) and Obed McCoy (2-29) had also earlier combined with Mayers to help restrict Chattogram to a moderate score.
Opener Josh Brown scored the highest 34 runs for the team with the help of two fours and three sixes in 22 balls, but his fluent innings could hardly be completed by other batsmen.
Shuvagata Home was the next best scorer with 24 runs from 16 balls, an innings which was crucial in taking the team past 100 after Barisal's bowlers faltered Chattogram.
Barishal will now play the Qualifier-2 game on Wednesday, which will be a virtual semi-final. Along with them will also be included the team which will have to taste defeat in the Qualifier-1 game.
Comilla Victorians and Rangpur Riders will face each other in Qualifier-1 on Monday night.