Bravo kept Pakistan’s victory bid on hold during his resistance-filled 410-minute long 116 and took a stunning two-handed catch from leg-spinner Yasir Shah to end his innings.
West Indies were finally bowled for 289 with just 12 over left in the match.
Bravo lingered on his haunches at the crease for a minute before trudging back to the pavilion, disappointed at his dismissal after bringing his team so close a draw or an upset win.
Bravo’s eighth Test hundred – spiced with ten boundaries and a six – had brought West Indies within 83 runs of victory and 27 overs to bat for a draw, after they were set a daunting 346 runs to win.
Left-armer Mohammad Nawaz trapped Devendra Bishoo before Miguel Cummins and last man Shannon Gabriel were run out, sparking wild celebrations among the Pakistan players.
Paceman Mohammad Amir finished with 3-63 and Shah took 2-113.
It was a fitting end to a match with no shortage of highlights, including a triple hundred (302 not out) by Azhar Ali, 8-49 by leg-spinner Bishoo and two fighting knocks by Bravo.
The win is more memorable for Pakistan as the match marked their 400th Test since they began the five-day format in 1952.
Pakistan captain Misbah-ul-Haq lauded the win.
“The way the Pakistan team is playing they are keeping Test cricket alive,” said Misbah, who now has 23 wins in 47 Tests as captain.
“Credit to West Indies, the way Bishoo bowled. Even in the first innings, they batted well. We got out cheaply in the second innings and got out to loose shots. Bravo was wonderful and fought hard.”
Earlier, Pakistan struck immediately on day five, Amir removing Marlon Samuels with the first ball of the day to have the tourists 3-95, but Bravo’s innings left them frustrated.
Bravo’s knock included two key partnerships, as he added 77 for the fifth wicket with Roston Chase (35) and then another 69 for the seventh with skipper Jason Holder who made 40 not out.
Pakistan had taken the second new ball with West Indies 6-224 and Bravo four runs away from triple figures.
He smashed an uppish drive off Amir’s first ball to backward point boundary to complete his magnificent hundred after 329 minutes of defiance.
Bravo and Holder had moved the Windies within 100 of victory in 41 overs at the dinner break, at 6-232.
The West Indian captain praised his team’s fight till the bitter end.
“It was a good fight, but still disappointed we din’t get over the line. Bishoo’s spell and Bravo’s knock were inspirational. Definite signs of improvement in performance,” Holder said.
The remaining two Tests will be played in Abu Dhabi (October 21-25) and Sharjah (October 30-November 3).