Somerset, who had won their first two games, made a flying start against Glamorgan at Cardiff as Tom Banton smashed 59 from 25 to guide them to 100-2 at the halfway stage of their innings.
But Banton fell to Mason Crane (3-42), who also removed James Rew and the defending champions slid to 171-9, with Australian all-rounder Nathan McAndrew taking 4-15 on his Glamorgan debut.
Carlson then flayed the Somerset bowling, hitting 109 from 45 as he and Will Smale – who shared an opening stand of 169 in this fixture two years ago – posted another century partnership, with Glamorgan cruising home in just 13.5 overs.
James Sales produced career-best T20 figures of 5-21 as Northamptonshire Steelbacks cruised past Gloucestershire by nine wickets to maintain their 100% start to the tournament.
Ben Charlesworth top-scored with 49 before he became Sales’ fifth victim in the visitors’ total of 164-9.
Steelbacks opener Chris Lynn then struck 69 from 36, his first half-century since returning to Wantage Road, sharing a partnership of 91 with fellow Australian Nathan McSweeney (53 from 36) before David Willey sealed victory in the 17th over.
Pakistan leg-spinner Usama Mir finished with 3-27 and seamer Tom Taylor 2-17 as Worcestershire hustled Warwickshire for just 141 at New Road, with only three visiting batters reaching double figures.
That target never looked enough for the Bears to defend and the home side made short work of it, Kashif Ali top-scoring with 36 before Sikandar Raza’s unbeaten 24 propelled them over the line with seven balls to spare.