England were 108 for two at lunch on the first day of the series opener, with Cook exactly 50 not out and captain Root, who won the toss, 40 not out.
Former skipper Cook and successor Root had so far added an unbroken 69 for the third wicket.
They joined forces at 39 for two after Test debutant Mark Stoneman and Tom Westley were both dismissed for eight.
The fifth day/night Test worldwide saw Root win the toss at 1:30pm local time (1230 GMT) under blue skies and on a good pitch.
After Cook got off the mark first ball, fellow left- hander Stoneman's first two scoring shots in Test cricket were both fours.
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.
Westley, still to cement his place at number three, was then lbw on review after missing a drive off first-change Miguel Cummins, with replays showing the ball would have smashed into the right-hander's middle and leg stumps.
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.
Cook drove Alzarri Joseph, one of four quicks in the attack, though the covers and Root handed out similar treatment to Holder, bidding to lead the West Indies to their first Test match win in England since 2000.
Disclaimer: No Business Standard Journalist was involved in creation of this content
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
