Somerset 351 (Dickson 70, Bartlett 55, White 5-77) and 56 for 1 (Lammonby 30*) beat Northamptonshire 180 (Vasconcelos 78, Overton 4-50, Henry 3-36) and 224 (Procter 87*, Henry 5-73) f/o by nine wickets
Henry, player of the match in Saturday's Vitality Blast triumph, continued to prosper with red ball in hand, finishing with figures of 5 for 73 and eight in the match.
Somerset duly knocked off the 54 runs required inside 11 overs before lunch to continue their winning ways, with Tom Lammonby powering six boundaries in an undefeated innings of 30.
Earlier, Procter and Tom Taylor (32) extended their seventh-wicket partnership to 53 before Henry trapped Taylor lbw to claim his fourth wicket of the innings.
With Australian overseas batter Sam Whiteman absent following the birth of his daughter last night, Northamptonshire were effectively eight wickets down and only six runs ahead. Procter, the last recognised batter, had already reached his half-century off 94 balls and, joined by Ben Sanderson, decided to take the offensive option against Henry and Craig Overton.
He quickly switched from rearguard mode into Bazball territory, hooking and powering balls through midwicket and mid-on. He played an audacious upper cut over the keeper's head off Overton, as well as playing some perfectly timed late cuts behind square.
Sanderson also played some expansive shots before he chipped a Henry delivery back to the bowler, the Kiwi taking a tumbling return catch to claim his fifth wicket.
Jack White supported Procter for a while but became Overton's third wicket when he pushed at a ball on off-stump and Tom Abell pouched the catch at first slip.
When Somerset began the chase, Lammonby drove Sanderson's second delivery down the ground for four, but he was dropped at third slip when he offered a difficult chance later in the over.
Sean Dickson drove White firmly through the covers for four but did not add any more to his total thanks to a lazy push outside off to a ball from Sanderson, keeper Lewis McManus taking a tumbling catch.
Abell took consecutive boundaries off White before Lammonby sealed the win by smashing Sanderson down the ground for four.