The 23-year-old Brathwaite, who was on the field for every minute of the test, was named man of the match.
"It was a privilege (to bat with Dowrich)," Brathwaite told the broadcaster. "The communication was good, we talked with each other, keep rotating the strike and we brought it home.
"This is the best batting match of my career... Obviously I've had a good start (to my career), you know the key is to maintain it," added Brathwaite, who has five hundreds and 12 fifties from 34 tests.
"I just want to continue working hard and score a lot of runs."
The victory ended a 13-match streak without a victory (10 losses and three draws) for West Indies, stretching back to May last year when they beat England at home. Pakistan won the three-match series 2-1.
"We took a lot of the momentum we had at the beginning of the game and ran with it," said Jason Holder, who helped set up his first win as West Indies captain with a five-wicket haul in the second innings.
"It's been something a long (time) coming. We've had some tough test matches in the last year. We're a young side in transition, we should take a lot from this series, not only from this match but we've done a lot of things good in this series."
Pakistan leg-spinner Yasir Shah claimed figures of 3-40 in the second innings and was adjudged the man of the series for his haul of 21 wickets while paceman Wahab Riaz, who had taken a five-wicket haul in the first, added two more to his tally.
Pakistan captain Misbah-ul-Haq felt Pakistan were well below par but also credited West Indies for the win.
"It's always disappointing to lose a test match. Yes, the series is important... You don't want to lose momentum," Misbah said. "We made a lot of mistakes, below our standards and poor I must say. Especially in batting, the discipline was not there."
(Reporting by Ian Ransom; Writing by Sudipto Ganguly in Mumbai; Editing by John O'Brien)
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