Put in to bat first, Sri Lanka posted 189-5, and England faced an adjusted target of 168 in 17 overs after rain held up the match for almost an hour. The visitors won with two balls to spare, taking an unassailable 2-0 lead in the three-match series.
Opener Pathum Nissanka (34 off 22) got Sri Lanka off to a fast start until Jofra Archer (2-42) bowled him, but Kusal Mendis (32 off 17) and Pavan Rathnayake (40 off 22) ensured that the hosts got to a competitive total.
Pacer Matheesha Pathirana (2-47) dismissed England opener Phil Salt in the first over, and Jacob Bethell (13) fell to Dasun Shanaka in the fifth over, leaving the twice T20 World Cup winners struggling at 38-2 as Sri Lanka smelled a chance to bounce back after Friday's loss.
But Banton, in at four, led the charge with captain Brook as England scored double digits in seven overs straight. Brook hit two boundaries and four sixes to score 36 off just 12 balls before he got caught trying to scoop a short delivery over the wicketkeeper's head.
Banton hit three sixes and four boundaries to score 54 off 33 balls in a player-of-the-match performance, as Sam Curran cleared the long-on boundary to pick up the winning runs, taking England to 173-4.
England and Sri Lanka will play again on Tuesday in their last game before both teams kick off their T20 World Cup campaigns next Sunday against Nepal and Ireland, respectively.