Hope was unbeaten on 147 at the close, an innings that has so far consumed six hours flat and lasted 252 balls, with 23 boundaries.
His counterpart Root was dropped at gully and successfully overturned an lbw decision during a tricky evening session.
While the West Indies' batting and bowling has improved markedly this match, their fielding remains fallible.
Was this a no-ball?
Stoneman had played solidly on the opening day before a loose drive against Kemar Roach and started confidently here with three boundaries in four balls in Roach's second over.
The tourists were ridiculed after a crushing loss at Edgbaston last week, but are on course for a first Test win on English soil for 17 years with two days remaining.
England will be more anxious about Westley.
Westley should have been run out for six after a mix-up with Stoneman.
Malan should have joined Westley in the pavilion after only four runs - a feather edge to wicketkeeper Shane Dowrich off Gabriel was not reviewed after a half-hearted appeal was turned down. Hope had made a career-saving, match-saving 90 off 209 balls against the guile of Yasir Shah on the fourth day of that Test.
The 25-year-old skipper's steady pace seems at odds with his 6ft 7ins frame, but he proved the value of accurate, full bowling on this pitch, having earlier also shown his quality with the bat with a series of exquisite drives.
That left England's batsmen with plenty of work to do and Alastair Cook's exit left two of their unproven rookies shouldering the burden, reaching tea 101 in arrears at 68 for one. Ben Stokes struck Hope on the helmet with a fi erce bouncer but the Windies pair refused to be intimidated as England became desperate for a wicket.
Anderson led the attack with five for 76 in 29 overs and is now a mere three wickets away from becoming the first England bowler to take 500 in Tests.
Anderson then found extra bounce to lure Dowrich into edging to Root at second slip.
But Holder survived Anderson's hat-trick ball with a solid forward defensive shot.
West Indies should have been eight down soon after but Moeen Ali dropped a simple chance at mid-on to dismiss Jermaine Blackwood on 21, Stuart Broad the unlucky bowler.
Blackwood, who in common with Holder hit seven fours, was then run out by Ben Stokes's throw to wicket-keeper Jonny Bairstow.
At tea, Mark Stoneman was 35 not out and Tom Westley four not out, with both batsmen needing big scores if they were to cement their Test places ahead of Ashes-holder England's upcoming tour of Australia.
"We want our balls back", chanted the crowd, as stewards led away the offending inflatables. I know that I'm good enough to play at this level so it's just about staying patient and being positive in the middle. It was the first 200+ stand for West Indies since Shivnarine Chanderpaul and Denesh Ramdin put on 200 at Hamilton against New Zealand in 2013.