Middlesex started the match with Gloucestershire in bottom place in the South Group but the England paceman took four for 24 in a 61-run win which lifted the county to third.
New Zealand quick Tim Southee took three for nine from three overs as the visitors to Uxbridge, chasing 162, slumped to their first-ever T20 defeat to Middlesex.
Captain Eoin Morgan hailed his pacemen, saying: “It was our best bowling performance of the tournament so far.
“Finn is crucial to us. It’s not easy for him being called up for Tests, not playing and having to come back and produce a different skill set. We’ve had a couple of consecutive games now where he’s not been called up and it’s allowed him to focus on what he’s doing well. He bowled fast tonight.”
Middlesex have not recorded back-to-back T20 victories this season but a win at Glamorgan on Friday could see them reach the quarter-finals for the second successive season.
Morgan added: “It’s often the best way to go through to the latter stages — teams who go on to win tournaments are often those who sneak through and build confidence in the latter part of the summer.”
The skipper was out for a duck as Middlesex made 161 for five, with contributions from Stevie Eskinazi (47), Paul Stirling (44) and Adam Voges (38).
Finn saw off Ian Cockbain and Cameron Bancroft in his second over and in his final over had Jack Taylor caught down the leg side for 31 and Benny Howell (34) caught off a skier by keeper John Simpson.