The leg-spinner finished with three for 13, while teenage seamer Blake Cullen returned a career-best three for 21 to successfully defend a score of 166 for seven at Lord’s.
That total was concentrated around Stephen Eskinazi’s 59 from 35 balls, making him the tournament’s leading scorer, but Middlesex still looked light on runs.
However, the Sharks – whose quarter-final hopes had already been dented by five washouts in their previous six games and whose squad has been hit this week by eight players having to isolate because of a positive Covid case in the camp – could only manage 103 for nine in reply.
Sussex inserted their hosts after winning the toss, but they looked understandably rusty in the field as Eskinazi and Max Holden, promoted to opener, built a solid platform during the powerplay. The pair shared a partnership of 85 from 54 balls, with Eskinazi placing his shots shrewdly as he passed 50 for the fourth time in as many Blast innings.
Holden swatted Tymal Mills’ first two deliveries for four and six, advancing to 38 before he holed out off Archie Lenham and when Eskinazi perished in similar fashion, scooping Will Beer to deep extra cover, Middlesex lost their way.
A tight over by Ravi Bopara – in which he dismissed the dangerous Daryl Mitchell with a slower ball – turned the tide, while Mills came back strongly from his earlier mauling to finish with two for 31. The Sharks conceded just 32 from their last six overs, along with collecting five wickets as Middlesex laboured to what looked a below-par total.
However, they swiftly removed both Sussex openers, with Luke Wright spooning Tom Helm to the diving Steven Finn, while Phil Salt drilled Mujeeb Ur Rahman straight to midwicket.
Mujeeb’s initial spell of three overs for 13 created pressure and Sowter compounded it by bowling Aaron Thomason with his first delivery – while Cullen’s second accounted for David Wiese, hooking into the hands of Holden at deep square leg.
Sussex’s best chance appeared to rest with Travis Head, who announced himself with a trio of boundaries off Helm, but the Australian was next to depart for 23, dragging a bottom edge from Cullen onto his stumps.
With Holden taking another running catch to dismiss Bopara off Sowter, the Sharks’ cause looked hopeless at 59 for six and so it proved, despite a promising knock of 22 by debutant Harrison Ward.