Electing to bat first, T&T gathered a sturdy 150 for nine off their 20 overs and then bowled out the English county for 106 in the Group, a fixture at Chinnaswamy Stadium.
"We went out there, we assessed conditions and we played how we wanted to play cricket," winning captain Daren Ganga said.
The result vaulted T&T to the top of the group on net run rate over Somerset, who had upset Indian Premier League (IPL) champions Deccan Chargers last Saturday.
Set 151 to win, Somerset were under pressure throughout after dipping to 28 for three after six overs.
The effervescent international all-rounder Dwayne Bravo claimed back-to-back wickets, dislodging Marcus Trescothick (3) and Craig Kieswetter (4) and spinner Sherwin Ganga sent back captain Justin Langer (15).
"It was a great team effort from everyone. Credit must be given to each and every player," Bravo said.