The Thunder made a meagre 6-128 but the Sixers' target was reduced to 84 runs from 12 overs after two rain delays at the SCG on Saturday.
Hughes - fresh from a superb unbeaten half-century against Adelaide - made 41no and Vince (43no) gently guided their side to victory, chasing down the revised target with nine balls to spare.
Their fourth win in a row elevated the Sixers to second spot with one game remaining and ensures they will return to the post-season for the first time since they lost the 2017 final.
They are now finding momentum at the right time of the season and in the hunt for their second title and fourth grand final appearance.
The home side's run chase got off to the worst possible start when Josh Philippe's horror night continued when he was run out first ball following an embarrassing mix up with Hughes.
Philippe earlier dropped a catch after racing 15m to try and dismiss Callum Ferguson after he skied a Steve O'Keefe delivery.
Hughes and Vince never looked in danger as they made light work of the pursuit.
The Thunder's total looked well below par after Sean Abbott snared the key wickets of Jason Sangha (5) and Anton Devcich (22) before he finished with 2-23 from his four overs.
Chris Green top-scored for the Thunder with 34no but couldn't find the accelerator and propel them to a competitive total late in the innings.
The Sixers' bowlers were particularly sharp at the death, taking three wickets and conceding just 38 runs in the final five overs.
Former internationals Shane Watson (28) and Ferguson (26) also made starts but crucially could not push on.