The skipper batted for 836 minutes to guide England to 569-8 at close on the fourth day to thwart Pakistan's pace-cum-spin attack on a flat Sheikh Zayed Stadium pitch.
But even on a docile pitch it needed a strong resolve from Cook as he came to the crease in the last hour of play on the second day under the pressure of a big total of 523-8 declared by Pakistan.
He finally played a tired looking sweep off spinner Shoaib Malik and was caught at backward square-leg by Shan Masood, ending his 528-ball knock which had 18 boundaries.
Pakistan's Hanif Mohammad holds the record of the longest Test innings with 970 minutes during his 337 against the West Indies at Bridgetown in 1958, ahead of South African Gary Kirsten's 878-minute knock during his 275 against England at Durban in 1999.
Jonny Bairstow made just eight before becoming Wahab Riaz's third victim, trapped in front of the wicket.
Left-arm paceman Riaz was the pick of Pakistan bowlers with 3-116 while spinner Shoaib Malik took 2-97.
It was a nightmarish pitch for the spinners as the first wicket to a slow bowler came in the 171st over when Malik bowled Stokes.
Pakistan's frontline spinner Zulfiqar Babar managed just one wicket in his 70 overs conceding 180 runs.
It was Cook's third double century that enlivened an otherwise dull day.
Cook flicked Riaz to backward square-leg for two to complete his double century off 395 deliveries, the second of the match behind Shoaib Malik's 245 for Pakistan.
Cook reached his 250 after tea, taking a single off Babar.
Root said Cook's long batting has set an example.
"Two days in that heat shows huge amount of skill, concentration and fitness," said Root of Cook's knock. "We spoke a lot about batting for long periods of time and how important its going to be to give ourseleves a chance of winning and our captain has led from the front.
Riaz admited Cook's knock had left bowlers frustrated.
"The way he (Cook) batted it was frustrating at times for me as a bowler," said Riaz. "He has got a great temperament and on this pitch he exhibited all his batting skills to the fullest."
Pakistan were once again sloppy in the field as they missed another chance to dismiss Cook when wicket-keeper Sarfraz Ahmed failed to take an inside edge off Riaz when the England captain was on 173.
Root also survived a confident leg-before shout when fast bowler Imran Khan trapped him but Pakistan's review once again went unsuccessful.
Root was finally trapped leg-before wicket by paceman Rahat Ali who finished with 1-73. Root hit seven boundaries in his 14th half-century.
Stokes also clobbered seven boundaries, reaching his fifth fifty and hit Babar for a four to give England the lead. He was finally bowled by Malik.
The remaining two Tests will be played in Dubai on October 22-26 and Sharjah on November 1-5.
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
