England were 215 for two at tea with Root, who won the toss, unbeaten on 103.
Former captain Alastair Cook was closing in on a century of his own at 85 not out.
The skippers past and present had added an unbroken 176 for the third wicket.
They had joined forces with England faltering at 39 for two after Test debutant Mark Stoneman and Tom Westley were both dismissed for eight.
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Root's fifty was his 11th in successive Tests -- a new England record and just one shy of South Africa star AB de Villiers's all-time leading mark of 12.
But while his conversion rate of fifties into hundreds has sometimes been a source of frustration to Root, this time the Yorkshireman went on to score his 13th century in 58 career Tests.
The fifth day/night Test worldwide saw Root win the toss under blue skies and on a good pitch.
He decided to bat first, for all the concerns about facing the pink ball and the difficulties of batting in twilight later on.
The 30-year-old eased Kemar Roach through the covers before clipping him off his pads.
It was an encouraging start by the Surrey batsman -- Cook's 12th England opening partner since Andrew Strauss retired five years ago.
But that was as good as it got for Stoneman, brought in after England dropped Keaton Jennings following a run of low scores during the preceding 3-1 home Test series victory against South Africa.
Roach produced a superbly sharp delivery that pitched on middle stump and clipped the top of off to clean bowl Stoneman and leave England 14 for one.
But Cook, who had a lucky break when he edged West Indies captain Jason Holder through a gap in the slips, and Root repaired the damage with a succession of boundaries.
Just before the lunch interval left-hander Cook, England's all-time leading Test run-scorer, completed a 74- ball fifty including 10 fours.
Root followed Cook to the landmark in 83 balls when a flashing cut off opposing skipper Holder flew through the slip cordon for four.
Root, who marked his first Test as captain with an innings of 190 against South Africa at Lord's last month, pulled off-spinner Roston Chase to the fine leg rope for a boundary that saw him complete a 139-ball century.
Cook then ended a dominant session for England by clipping Roach through midwicket for four.