The pair put on their match-winning partnership in 92 balls for the Trinbago Knight Riders against the Barbados Tridents at Queen’s Park Oval.
Amla went on to score 81 from 54 balls having brought up his half century from 42 balls.
Bravo made an undefeated 66 with both men hitting four sixes.
They took their side from what looked like certain defeat to victory in 15.2 overs.
Trinidad made 170-5 off their 20 overs before restricting Barbados to 159-8 for an 11-run win.
The previous record for a fifth-wicket partnership in T20 cricket was 149 set by Yogesh Takawale and Sairaj Bahutule in the Indian Premier League in 2007.