Brathwaite's all-round brilliance, both in actual play and later in the Super Over, finally broke Trinbago's four-match winning streak.
Ali will no longer be available, though he failed to get a game this season, owing to domestic commitments.
Akeem Jordan picked four wickets on his T20 debut while Evin Lewis smashed 65 off 30 balls to help Patriots register their 2nd win.
Chadwick Walton remained unbeaten on 51 in Jamaica Tallawahs' successful chase of the target of 141.
Qais Ahmad and Imran Tahir shared five wickets between them to bundle out St Kitts and Nevis for just 121.
Hasnain, who has played only two first-class matches, is a part of Sindh's First XI side captained by Sarfaraz Ahmed.
Colin Munro and Lendl Simmons smashed rapid fifties while a blazing cameo from skipper Kieron Pollard helped Trinbago post 267-2.
Cornwall, promoted to open the innings, launched a frenzied attack to lead his side to a comfortable five-wicket win over Jamaica Tallawahs.
Sandeep Lamichhane returned impressive bowling figures of 3-22 as Barbados secured an 18-run victory over SKNP.
Abid Ali, Sami Aslam headline Quaid-e-Azam Trophy opening round with double tons
Rahkeem Cornwall smacks 75 off 30 balls
Jofra Archer earns ECB central contracts, Moeen Ali loses Test deal
Labuschagne puts his weight behind Warner despite below par Ashes campaign
Kohli, Chahar complete comfortable win for India
Malik blitz spurs Guyana to fifth win on the trot
Babar Azam elevated to vice-captain post
Sami Aslam starts domestic season with a bang
Akmal and Shehzad part of probables for Sri Lanka series
Misbah to give leeway to Umar Akmal