Unwell before the match and requiring medication to settle an unhappy stomach, Vince hit 101 from 58 balls at the SCG to win the battle of the Brits over the equally hard-hitting Ben Duckett.
The successful chase with eight wickets to spare was the eighth biggest in the 14-year history of the BBL, and the biggest in any match at the SCG.
It also kept the Melbourne Stars winless after four games with their finals hopes fading fast, while the Sixers remain undefeated after three matches.
"I didn't feel 100 per cent," Vince said.
"It was nothing major, I just felt a bit off. I didn't throw up or anything.
"Batting second was handy, it let the medication set in. But once I got moving and the tablets kicked in, I felt better."
For stages on Boxing Day, the Stars appeared the team on top in front of a crowd of 23,212.
Duckett was all power for the visitors, bringing his blend of Bazball to the Big Bash with 68 from 29 balls.
England's destroyer became only the second player in BBL history to hit six fours in an over, unleashing a flurry of pull shots and reverse sweeps off spinner Akeal Hosein.
He also took to fellow spinner Todd Murphy, launching a big slog-sweep for six to bring up his half-century off 22 balls.
Englishman Ben Duckett had an impressive all-round match for the Melbourne Stars. (Mick Tsikas/AAP PHOTOS)
Jackson Bird copped similar treatment with two straight fours and a six on the next ball, before having the left-handed opener caught at deep third man.
Glenn Maxwell also hit 32 off 17 for the Stars, who were at one stage 3-126 after 10.2 overs before Murphy (2-26) and Ben Dwarshuis (2-33) pegged them back.
And while the Stars took only 16 from their two power-surge overs and fell away late, the Sixers did the opposite with the bat.
After Josh Philippe (42 from 23) and Vince put on 83 for the first wicket inside eight overs, the hosts went even quicker in the second half of their innings.
Jordan Silk (34no) and Vince took 35 off their two power-surge overs from Peter Siddle and Maxwell, with Vince in particular going after the latter.
The Englishman hit four sixes in total, with two coming off Maxwell, one deep over mid wicket off Tom Curran and another when he hit fingerspinner Doug Warren inside out over cover.
The opener reached the rope another 12 times in his knock, registering more boundaries than he did dot balls to keep the Sixers' chase well and truly on track.
The 57-ball century made Vince only the second player to bring up three figures in Sixers colours, after narrowly missing out a hundred in the 2021 final.
"It's nice. I think I have thrown a couple away with a few 90s in the past," Vince said.
"It's a nice feeling to be able to get the three figures for the Sixers finally, but even nicer to get the win.
