When play began, Nottinghamshire led by 127 with seven wickets in hand, but it was soon clear there was more than enough in the pitch for a seam attack of Yorkshire’s quality to inflict more damage.
White struck with the fourth ball of the day, finding the outside edge as Jack Haynes defended his off stump.
He quickly chalked up another scalp when he drew Ben Martindale into a drive outside off stump and caught the edge again, Dom Bess snaring the catch at third slip.
Mitchell Hay was beaten past the inside edge to be leg before as White claimed his third of the day, while Coad took two in two balls as Bess grabbed two more catches to remove Liam Patterson-White and Brett Hutton.
Tom Giles, Nottinghamshire’s injury replacement for Olly Stone, became victim number five for White before Lyndon James was cleaned up by Coad to complete the destruction in just short of an hour-and-a-half.
Leading wicket-taker George Hill, needing two more to total 50 first-class wickets or more for the second season running, did not get a look-in.
Chasing 158 should have been plain sailing, especially with Stone out of the game after feeling hamstring discomfort following his first-innings five-for.
Openers Luxton and Adam Lyth gave the innings a solid foundation with 54 in 12 overs before Lyth pushed at one outside off stump from Hutton and was caught behind.
Hutton then removed Sam Whiteman via a thin outside edge before left-arm spinner Patterson-White had James Wharton leg before.
Luxton, who had just completed a half-century from 78 balls, lost his composure and was caught off a top edge with an attempted pull, but needing just 50 more at tea with six wickets in hand, Yorkshire remained strong favourites.
Yet Pakistan seamer Ali bowled Matt Revis with one that shot through and had Dom Bess caught at slip, either side of Hill falling stumped, to turn the pressure up still further.
Bairstow drew on his experience – and mental toughness – hitting two fours and a six in one Ali over, then swishing and missing at four balls of the next before getting the job done.
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Nottinghamshire head coach Peter Moores:
“It was a really good game of cricket. We’d be frustrated because we missed out in the third innings really.
“This morning, the ball didn’t do masses, but just did enough to catch the edge. The way White and Coad bowled, they just put a lot of balls in the right area and we edged them. Some days you get away with it and we didn’t today, so I think I give them a lot of credit.
“From 127 in front for three down overnight, any sort of partnership would have set up a really challenging run chase for them.
“If we’d had Olly Stone out there, we’d have been probably favourites, I think, the way he’s bowling at the moment. We didn’t bowl as well with the new ball as we would have liked but we didn’t fall away and that’s the nature of this team.” C
Yorkshire captain Jonny Bairstow:
“It’s two good teams going toe-to-toe and that’s exactly how it should be. So winning this meant a lot to us.
“Look, we’ve owed it to ourselves this year. We’ve been below par with the bat, and that’s every single one. There’s been too many times George and Bessy have bailed us out throughout the year.
“The teams that we haven’t fronted up against this year are actually the teams that have gone down, which is such a shame, really. So, yeah, it does mean a lot.
“It meant a lot to me to be there to win the game. I felt I needed to do that for the lads after coming back from the Hundred because there were a few bits with that, which I think is partly from a technical point of view, that set me back a little bit.”
