Set 130 to seal a clean sweep in the series, thanks to the batting heroics of debutant Razaullah, they were given a scare on the fourth morning when Mohammad Abbas removed both openers for nought in the first over.
It was the kind of challenge they needed after doling out thrashings at Headingley and Lord's and Root came together with Jordan Cox to ensure they were not found wanting.
The pair shared an unbeaten stand of 128 to rack up a comfortable eight-wicket success, Root benefitting from a couple of reprieves to find form with 62 not out and Cox capping his positive start to life in the Test arena with an accomplished 59 not out.
That secured England's best result since they beat the West Indies by the same scoreline in 2024 and gave Root a solid foundation to build his new captaincy reign on.
Sterner examinations await over the winter, in South Africa and Bangladesh before a one-off match in Melbourne, but after picking up the pieces following Ben Stokes' chaotic retirement, Root can at least claim to have steadied the ship.
Any chance England had of making life easy on themselves evaporated instantly, Abbas straight on the money from round the wicket and Ben Duckett unable to avoid the nick outside off.
It was the latest in a string of failures for the left-hander, whose average for the series plummeted to just 8.80. Duckett is England's only centurion of the summer, having hit 113 against New Zealand at Trent Bridge, but bows out in a clear rut.
The pressure is also on his opening partner Emilio Gay, whose stock rose with a hard-fought 60 in the first innings only to dip again as Abbas pinned him lbw for a four-ball duck.Â
A third breakthrough would have been huge but Pakistan could not force one through, Cox surviving a dicey run to get off the mark and Root edging his first ball from Razaullah for four through the slips.
Root put another couple of short balls away to get the scoreboard moving but the game-changing moment arrived in the 10th over when he dragged down his stumps attempting a booming drive, only for Mohammad Ali's celebrations to be cut short by a no-ball signal. It was the seamer's 17th front-foot error of the series and easily the most costly.
Having been spared on 23, Root had another life on 34, edging Abbas between first and second slip with both catchers leaving it for the other.
Root brought up his fifty off just 57 balls, a compact cut for his seventh boundary, with Cox close behind in 61 deliveries.
Pakistan's fight, having belatedly reared its head on Friday, was gone now and it was apt that Cox's winning run came off a misfield, the final error in a tour littered with them.
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