Archer helped end the last remaining 100 per cent record in the Vitality Blast as Kent were defeated at Hove thanks to unbeaten half-centuries from Laurie Evans (65) and Philip Salt (63).
Archer conceded 20 in his first two overs but recovered to snare Kent's Adam Milne for a duck and finished with one for 28.
Sussex chased down Kent's 154 for eight with room to spare for a thumping nine-wicket win to move up to second in the South Group.
Tom Westley top-scored with an unbeaten 86 to fire Essex to a 25-run win over Gloucestershire.
Cameron Delport and Dan Lawrence also contributed half centuries to propel the visitors to an imposing 206 for three, and Gloucestershire came up short at 181 for five.
Tom Banton cracked a breathtaking 71 from just 37 balls as Somerset beat Surrey by eight wickets at Taunton.
Set 204 to win, the hosts got home with eight balls to spare, Banton smashing 11 fours and two sixes, while Eddie Byrom marked his Somerset T20 debut with four sixes in a whirlwind 54 not out off 19 deliveries.
Spinners Mason Crane and Liam Dawson took three wickets apiece as Hampshire beat winless Glamorgan by 41 runs.
Liam Livingstone starred with both bat and ball to help Lancashire stretch their lead at the top of the North Group, defeating Durham by five wickets.
The 25-year-old spun his way to two for 21, while Matt Parkinson took
four wickets to bowl out the hosts for 139.
Livingstone then blasted the Durham attack around the park with 70 from 48 deliveries to guide Lancashire over the line.
Worcestershire's Riki Wessels hit a superb 91 as Yorkshire, defending 178, were ultimately brushed aside by five wickets with 15 balls to spare at Headingley.
The Vikings lost their third game in six despite being 104 without loss in the 12th over thanks to openers Adam Lyth (68) and Tom Kohler-Cadmore (40).
Wayne Madsen's 28-ball 50 took Derbyshire home as they chased down 181 to beat Northamptonshire by six wickets with two overs to spare at Wantage Road.
A fine 69 from 42 balls by Tom Moores helped Nottinghamshire to 184 for four against Birmingham Bears, who were then skittled out for just 113 with Matt Carter taking three for 14.
