England were 171 for three in their second innings at stumps on Sunday's third day, a lead of two runs, after the West Indies had made an impressive 427 in their first innings.
Root, dropped on 10, was 45 not out on his Yorkshire home ground, with Dawid Malan unbeaten on 21.
Their unbroken stand was so far worth 77 runs.
Pace-bowling all-rounder Holder who had earlier made a valuable 43, captured the key wicket of Alastair Cook and removed Tom Westley on his way to stumps figures of two for 44 in 17 overs.
England, facing a large first-innings deficit of 169 runs, saw Cook and Mark Stoneman, who along with fellow batsman Westley and Malan is looking to cement his Test place ahead of the upcoming Ashes tour of Australia, start steadily.
Stoneman, Cook's 12th opening partner in five years since the retirement of Andrew Strauss, did, however, hit three fours off as many balls from Kemar Roach.
But the more defensive Cook, England's all-time leading Test run-scorer, fell for 23 to end a stand of 58 as Holder, maintaining an excellent line and length, eventually found the left-hander's outside edge and had him caught behind.
- Stoneman fifty -
Number three Westley should have been run out for six after a mix-up with Stoneman.
He failed to cash in though, falling for eight when caught behind driving loosely at Holder.
But Stoneman, hit on the left hand by Holder on 35, completed a maiden Test fifty in his third innings at this level.
The 30-year-old Surrey left-hander was bowled soon afterwards, however, for 52 by an excellent delivery Shannon Gabriel that pitched in line and hit off stump.
The fast bowler had an anxious wait as the umpires checked for a no-ball before it was confirmed that England were 94 for three.
Malan had a lucky break on four when the West Indies opted against reviewing a rejected caught behind appeal off Gabriel, although technology indicated a thin edge.
While the West Indies' batting and bowling has improved markedly this match, their fielding remains fallible.
For the second time in the match they dropped Root early in his innings when he fended at the luckless Roach only for Kyle Hope to floor the gully chance.
Root, dropped on eight en route to 59 in England's first innings 258, drove Holder for four and struck Roach through the covers for another boundary.
- Holder denied -
But when he missed a legside clip off Holder on 35, he was given out lbw.
Root, however, reviewed immediately and was spared when replays indicated the ball was missing leg stump.
Holder was again unfortunate when his lbw appeal against left-hander Malan, then on 12, was rejected by umpire S Ravi.
He reviewed the Indian official's verdict but replays ruled it was 'umpire's call'.
West Indies' innings represented a remarkable turnaround given they had been dismissed for just 168 and 137 during an innings and 209-run defeat at Edgbaston last week in the first of this three-Test series.
They resumed on 329 for five, a lead of 71, only for James Anderson to take two wickets in two balls as Shai Hope was caught behind for his overnight 147 to end a brilliant maiden Test century, with Shane Dowrich held by second slip Root.
Anderson led the attack with five for 76 in 29 overs and ended the innings just three wickets away from becoming the first England bowler to take 500 in Tests.
But Holder, who survived Anderson's hat-trick ball, and Jermaine Blackwood, who made 49 after being dropped on 21, frustrated England with an eighth-wicket stand of 75, as they extended the tourists' lead beyond 100.
First Published: August 27, 2017, 11:28 PM IST