Yorkshire, who have never lifted the domestic T20 trophy, successfully chased 168 to beat Notts Outlaws at Trent Bridge.
England opener Ben Duckett was one of several Notts batters unable to kick on to a big score after getting a start – he was dismissed for 29 in Notts’ 167-7.
Yorkshire were 11-2 in the second over but were easy winners in the end, thanks to a third-wicket partnership of 144 between Bairstow (83 not out) and James Wharton (55).
Elsewhere, Derbyshire Falcons fell just short of their victory target of 204 against Durham.
Matt Montgomery (74 not out) was on strike for Matthew Potts’ final delivery of the innings with a six required to tie, but the England seamer bowled an excellent dot-ball yorker.
The remaining two North Group teams lost to sides from other groups.
Lancashire Lightning were well beaten by Surrey, who are bidding to win England’s domestic T20 competition for the first time since the inaugural edition in 2003.
Jason Roy’s 45 off 19 balls got Surrey off to a fine start, Ollie Pope made 31 and Tom Curran smashed an unbeaten 49 off 20 balls as the home side posted 213-6.
Roy took a superb slip catch to dismiss Keaton Jennings first ball – one of two scalps for left-arm paceman Reece Topley (2-27) in the opening over of the visitors’ reply – and Lancashire were eventually bowled out for 154.
Meanwhile, unbeaten half-centuries from Nick Kelly and Ben Cox were not enough for Leicestershire Foxes as they lost by 18 runs to Worcestershire Rapids.