Jacks opened the innings with a 15-ball fifty as Surrey powered their way to 76 without loss in the powerplay.
Further contributions from Jason Roy (45), Jamie Overton (27) and Tom Curran (25) saw Surrey reach 223 for seven from their 20 overs.
In reply, Paul Stirling hit 58 before being run out, but Middlesex were always behind the rate from there and after Eoin Morgan holed out for 32, it was all over.
Opener Finn Allen made an unbeaten 73 off 51 balls as Lancashire made it two wins out of two with a 16-run victory over Leicestershire.
Allen batted through his side's innings of 172 for eight and that total proved too many for the visitors, who finished on 156 for five despite Scott Steel's 54 not out.
Gavin Griffths returned a career-best four for 24 for Leicestershire, but disciplined bowling from Lancashire kept the Foxes in check and not even 32 from 17 balls down the order from Rishi Patel could turn the tide.
Jonny Bairstow top-scored with 34 off 22 balls as Yorkshire eased to a 145 target and an opening-night win over Birmingham Bears at Emerald Headingley.
The Vikings secured a routine six-wicket victory to begin their North Group campaign with a bang as Bairstow shared 58 for the second wicket with England colleague Dawid Malan.
They fell in the seventh and ninth overs – Malan for 23 – as the score slipped to 69 for three before Tom Kohler-Cadmore, Harry Brook and Will Fraine saw their side home with nine balls left.
Jordan Thompson equalled a career-best three for 23 from four overs of seam as the Bears stuttered to 144 for eight, with Sam Hain's 59 off 41 holding things together.
Marnus Labuschagne's superb unbeaten 93 off 56 balls could not stop Gloucestershire from starting their campaign with a four-run win over Glamorgan.
Glenn Phillips' 44 and 30 from Benny Howell off 15 balls saw Gloucestershire post 179 for six in Cardiff, which always looked like being a challenging total.
And, despite Labuschagne making a career-best Twenty20 score on his Blast debut, Glamorgan fell just short against some tidy Gloucestershire bowling.