The West Indies chased down a seemingly tough target of 322 with more than four overs to spare on Tuesday's final day.
Shai Hope led the way with 118 not out as the West Indies won a Test in England for the first time in 17 years.
None of Hope's previous 11 Tests had yielded a hundred.
But this match saw the 23-year-old Barbados batsman score two, with Tuesday's knock following his first-innings 147.
Opener Kraigg Brathwaite fell just five runs short of also scoring twin hundreds at Headingley, combining with Hope for two partnerships worth 390 runs in total, including a key stand of 144 on Tuesday.
The West Indies will now head to Lord's for next week's third Test all square at 1-1 in the three-match series following a win made all the more remarkable by their humiliating innings and 209-run defeat in the first Test at Edgbaston.
That inept display prompted West Indies great Curtly Ambrose to label the current side "embarrassing" and "pathetic".
"It feels really good, especially after the game in Edgbaston, it was a tough loss," Holder told reporters after an astonishing fifth day in Leeds.
"A lot of teams would have crumbled coming back into the second Test match and probably would not have given England the fight that we gave them," the towering all-rounder added.
"I said at the beginning of this Test match that I back these guys to rebound and there was no better way to do it."
The aptly-named Hope, the first batsman to score two hundreds in both innings in 127 years of first-class cricket at Headingley, was proud to have played his part in a morale-boosting success.
"It was mainly about winning the game, especially after the loss at Edgbaston.
"Knowing how much the fellas really wanted this win, you could see the fight and belief in the dressing room on the faces of the guys," added Hope, the first West Indies batsman since Gordon Greenidge at Old Trafford in 1976 to score hundreds in both innings of a Test in England.
When Joe Root declared England's second innings on 490 for eight late on Monday, allowing his bowlers to have six overs before stumps on the fourth day, few pundits thought he had made a major mistake on his Yorkshire home ground.
And Root, set to lead England in their Ashes defence in Australia later this year, insisted this experience would not stop him declaring again in similar circumstances.
"I don't think it will," he said. "The declaration might not have been timed right but I thought it was a positive thing to do, we're a side that want to go out there and win Test matches."
Both sides dropped several catches each, with England's missed chances ultimately proving the more costly.
"We have to be better, we know that taking early wickets and taking opportunities to put sides under pressure is a massive part in winning Test matches," said Root.
If he needed a consoling word, Root could perhaps turn to former England captain David Gower. In 1984, Gower's final-day declaration left the West Indies needing 342 to win a Test at Lord's.
Yet they got them for the loss of just one wicket as outstanding Barbados opener Greenidge, with an unbeaten 214, and the under-rated Larry Gomes (92 not out) made a mockery of Gower's move.
It was a match referenced by West Indies bowling coach Roddy Estwick after stumps in Leeds on Monday.
"I remember in 1984, we were set 300-odd and Gordon Greenidge got 200-odd and we won that Test match. So hopefully tomorrow the boys can come out and go well."
First Published: August 30, 2017, 9:53 AM IST