The visitors had to twice come from behind after taking the lead in the first half, before a Tony Cascio goal in the final minute of stoppage time.
The attacking football eventually led to a goal when Atiba Harris was on hand to head in from Powers's corner.
It was a corner that helped to draw Montreal level shortly afterwards, as Hassoun Camara reacted quickest to tap the ball in from close range.
Edson Buddle missed a great chance to put the visitors back in front prior to half time, but he could only hit the post and was made to pay when Montreal broke away at speed. Di Vaio found Daniele Paponi on the edge of the box and the striker smashed the ball into the top corner.
Colorado got back on level terms around the hour mark when Powers found space in the box and fired past the goalkeeper with a good first touch.
Montreal took the lead again when Paponi got his second of the game, finishing off a quick counter-attack from close range, before yet another equaliser from Colorado. Deshorn Brown got on the end of Klute's cross to fire the ball home 10 minutes from time.
A dramatic finish was on the card and so it proved to be when, in the 96th minute, Cascio founds space on the edge of the box and fired home to seal all three points for the Rapids.