Somerset 183 for 8 (Babar 114*) beat Glamorgan 117 (Overton 3-36) by 66 runs
Babar Azam's career-best 114 not out from only 62 balls set up a convincing win for Somerset in Cardiff, maintaining their outside chance of qualifying for the quarter-finals.
They also improved their net run rate, with Glamorgan losing ten wickets with 25 balls of their innings remaining.
The Glamorgan bowlers weren't at their best, and the fielding was sub-standard, with Babar dropped twice. He then made the home team suffer as he guided his team to a total far beyond the par score at Sophia Gardens this season.
Glamorgan's reply was a pitiful affair from the moment they lost their first two wickets in nine balls balls, with the game over as a contest when they collapsed to 47 for 5, and then 62 for 6 at the halfway stage.
Somerset, who were put in on the same slow pitch where Glamorgan defeated Northants the previous Sunday, lost two wickets in the opening three overs and were 39 for 2 after the Powerplay.
Steve Davies was the first to go when he was stumped from Prem Sisodiya's quicker ball, and in the following over 18-year-old Will Smeed, who made 82 against Gloucestershire last week, mistimed an intended pull to give mid-on a simple catch.
Babar, who was dropped from a difficult chance to cover on 10, scored freely on either side of the wicket, and reached a rapid fifty from 34 balls, and put on 52 with Tom Abell for the third wicket, before the Somerset captain lifted Andrew Salter's offspin to long-off.
Babar was reprieved on 67, when Marchant de Lange, whose first over went for 18 runs, had him dropped at third man, where Owen Morgan misjudged a top-edged cut. He was well supported by Lewis Goldsworthy, the 18-year-old debutant who impressed bowling left-arm spin in England's U-19 World Cup campaign.
Babar reached his century in the 19th over, the second fifty coming from just 23 deliveries, with the partnership for the fourth wicket yielding 110 in 10.4 overs. He also reached the landmark of 5000 runs in T20 cricket, becoming the third-fastest man to get there after Chris Gayle and Shaun Marsh.
Roelof van der Merwe started Glamorgan's demise by having David Lloyd and Chris Cooke caught at backward point in his opening over, both by the substitute fielder George Bartlett. They reached 38 for 3 off the Powerplay, but the rot then set in as the batsman found ways of getting themselves out.
Morgan top scored with 24, but there was little resistance from the others, with the margin of victory testament to Somerset's overwhelming superiority.
Matt Maynard, Glamorgan's coach, rued his side's slipshod effort in the field. "Catches win matches, and when you drop the world's best T20 opener in the third over, you are going to suffer," he said.
"I have been involved here for some years and have spoken about this, and nothing has happened. The fielding tonight was poor, and it has to improve."