Sri Lanka chasing 377 for victory ended on 193 for 2 after both captains decided a result was not possible an hour before the end of today's final day of play.
Dimuth Karunaratne scored 75 and Oshada Fernando an unbeaten 66 against disciplined bowling from the home side that restricted the visitors to 164 runs for the loss of two wickets from the 70 overs bowled today.
However, Brathwaite was awarded the Man-of-the-Match award for his knocks of 126 and 85 that helped bat the visitors out of contention.
"Pleasing winning the award - as captain want to lead from the front,” Brathwaite said afterwards.
“(The) main thing for me was to keep it simple. Bat most balls. Made sure I had a solid plan. I could change my batting style at times, but I am confident I can score at whatever rate I choose to.”
He praised his teammates for the resilience especially in light of the nature of the pitch that was kinder to the batsmen.
“Both pitches were good pitches. But happy guys didn't give up, up to the last spell. Batting 90-plus overs is great. Happy with the attitude and discipline. Happy with the attitude of the bowlers."
Resuming from their overnight total of 29-0 from the nine overs they faced on Thursday evening, Lahiru Thirimanne and Karunaratne took the score to 101 when Thirimane edged Alzarri Joseph to Rahkeem Cornwall at slip. He made 39.
As evidence of how tight the West Indies bowling was Sri Lanka scored 45 runs in the following 17 overs before Kyle Mayers trapped Karunaratne lbw for 75.
However, that was the last wicket to fall on the day as Fernando and Dinesh Chandimal took the score to 193 before play was called off.
Joseph finished with figures of 1-33 while Mayers had 1-5 from the six overs he bowled.
Suranga Lakmal was named player of the series for his 11 wickets.
Happy. I really want to win games, and bowl accordingly - that's what I like to do,” he said. (The) wicket was helping a bit, but I know how to bowl on such wickets. Bowl in right areas and challenging the bowlers is my style."
The two-Test series ended 0-0 as the first Test also ended in a draw.
At the close of play, Karunaratne, who was dropped on 14 by Jermaine Blackwood, is on 132 and De Silva on 56. Together they have so far put on 97 for the fourth wicket as Sri Lanka eye a massive first innings total on Monday.
After winning the toss and choosing to bat, Sri Lanka got off to a slow start but gradually built momentum throughout the day.
Karunaratne and Nissanka opened the batting and crept to 61-0 without loss at lunch. The 50 partnership came off 132 balls as the home side took a more cautious approach against the West Indies bowling led by Shannon Gabriel.
The partnership would endure until after the interval when Gabriel induced an edge from Nissanka, who was caught at slip by Rahkeem Cornwall for 56 and with the score at 139.
The West Indies would make further inroads fairly quickly afterwards when at 164-1, Roston Chase dismissed Oshado Fernando for three and then at 170-2 removed Angelo Matthews also for three.
However, that was the last success the West Indies bowlers would have for the remainder of play.
Gabriel has so far taken 1-56 from 12 overs while Chase has 2-42 from 17.
Joe Root's record-equalling 33rd red-ball century had ensured England ended a difficult opening day with a chance to build a commanding lead, and they did just that early on as Atkinson took centre-stage.
Resuming at 74 not out, Atkinson brought up his maiden Test century with a fine drive past mid-on shortly before lunch, eventually ending his knock with 14 fours and four sixes.
He would later fall for 118 to the outstanding Asitha Fernando, who then completed a five-for by removing Olly Stone to wrap up the England innings at 427 all out.
Any hopes Sri Lanka had of making an early dent in that target were frustrated, however, as England shared the wickets around in a brilliant team bowling performance.
Chris Woakes and Stone, who removed Dimuth Karunaratne and Pathum Nissanka within the space of five balls – left the tourists teetering at 35-3 by the end of the 10th over, and there was little help to come from the middle order.
Matthew Potts took the ball and sent stumps flying to account for Angelo Matthews and Dhananjaya de Silva in the 21st over, with Woakes, Stone and Atkinson later also doubling up as the tourists collapsed.
Kamindu Mendis' steady knock of 74 off 120 balls brought some respite for Sri Lanka, but he edged Atkinson's delivery into the palms of Woakes for the final wicket, failing to match his ton from the first Test at Old Trafford on a miserable day for the visitors.
England then avoided any drama when taking up the bat for seven overs before stumps, and Ben Duckett (15) and Pope (2) will resume at the crease on Saturday, hoping to make their handsome lead an unassailable one.
Data Debrief: Atkinson's big moment
While Root's heroics put England in a decent position ahead of Friday's play, Atkinson's brilliant 118 – coming off 115 balls – could prove the difference in this Test, allowing England to build a strong lead despite a lack of support from the lower order.
Atkinson's previous best red-ball knock was a score of 21 not out versus West Indies at Trent Bridge in July.
Chasing a target of 233, Man-of-the-Match Hope scored 110 and Lewis featured in an opening stand of 143, a record-opening stand for the West Indies against Sri Lanka in the West Indies, which was ended when the latter was bowled by an in-swinging yorker from Dushmantha Chameera for 65.
Lewis had faced 90 balls in his 109-minute stay at the crease hitting four fours and two sixes.
Hope, who dropped from the West Indies Test squad last year for loss of form, was a picture of composure, facing 136 balls from which he hit 12 fours and a six in his 10th ODI century before he, too, was bowled by Dushmantha Chameera who finished with 2-50 from his 10 overs.
Hope also shared in a 72-run second-wicket stand with Darren Bravo who hit two fours and a six and in his unbeaten on 37 at the end. With him was Jason Mohammed, who was not out on 13.
Sri Lanka would have been disappointed after winning the toss and opting to take first strike, were given a solid platform of 105.
The partnership was broken two balls into the 20th over by Kieron Pollard, who brilliantly caught Dimuth Karunaratne off his own bowling for 52. He had faced 61 balls and struck four fours in his 89 minutes at the crease.
Eleven balls later it was 112 for 2 when Danushka Gunathilaka, who was going well on 55 when he was controversially given out for obstructing the field, ending his 98-minute stay at the crease during which he struck seven fours from the 61 balls he faced.
The incident seemed to rattle Sri Lanka as two run-outs (Pathum Nissanka and Angelo Matthews) followed that saw Sri Lanka slide to 126 for 4.
Ashen Bandara scored the third half-century of the Sri Lankan innings that provided some stability to the lower order but by then the run rate had fallen before five runs and over and he was without a partner who could successfully take on the West Indies bowling attack.
His was the ninth wicket to fall in the 48th over bowled by Jason Holder for an even 50 that included four fours.
Holder, who also accounted for the wicket of Chameera returned figures of 2-39. Jason Mohammed, who was introduced into the attack late had 2-12 from his four overs having claimed the wickets of Kamindu Mendis and Wanindu Hasaranga de Silva.
There was a wicket each for Alzarri Joseph, Pollard and Fabian Allen, in a performance of which Coach Phil Simmons would be proud.
On a day when only 34.4 overs were possible after play began after tea, Sri Lanka’s openers Pathum Nissanka and Dimuth Karunaratne shared in an opening stand 106.
Roston Chase broke the partnership in the 31st over when he had Karunaratne caught and bowled for 42. The Sri Lankan captain who had scores of 147 and 83 in the first Test, was early into a drive and ended up scooping the ball back to Chase, who dove low to his right to snag the catch, leaving Karunaratne eight runs short of a possible seventh score of fifty or more in Test cricket.
When bad light brought about the end of play Nissanka was on 61 and Oshada Fernando on two.
Chase ended with figures of 1-33 from 7.4 overs. Jomel Warrican 0-7 from six overs and Kemar Roach 0-12 from six overs were the most economical bowlers for the West Indies.
West Indies made two changes from the team that lost the first Test with Rahkeem Cornwall and Shannon Gabriel making way for Kemar Roach and Veerasammy Permaul.
Charith Asalanka makes his Test debut for Sri Lanka, who have a 1-0 lead in the two-Test series.
