Somerset won the toss chose to field on a grey and cold night at Lord’s, and Meredith, and his opening bowling partner Craig Overton (2-21) tore into the Middlesex line-up immediately.
After eight overs, the hosts were 33-6, losing wickets off the first ball of the second, third, fourth and fifth overs.
Josh Davey (2-13) and Ben Green (2-17) then combined to mop up the remaining wickets inside 17 overs.
Somerset lost Will Smeed early, and the normally aggressive Banton and Kohler-Cadmore batted maturely in an unbeaten stand of 78 to see the visitors home to a third win in five games.
Banton mixed quick running between the wickets with selective power hitting, finishing with a flurry after a six to deep mid-wicket and a reverse sweep behind square.
He was assisted by Kohler-Cadmore, who went at a run-a-ball in his unbeaten 30.
The defending champions have now won back-to-back matches in the competition, after thrashing Hampshire on Sunday, and go above Sussex and Surrey at the top of the table on net run rate.
Middlesex, whose total was two runs fewer than their previous lowest score of 80, set against Kent in 2021, have now lost four of their five group matches and are bottom of the pile.