White's goal canceled out an earlier corner kick header from Danny Wilson, as the Whitecaps moved up a spot into ninth in the Western Conference standings and four points adrift of the seventh and final West playoff spot.
Maxime Crepeau made four saves for Vancouver (7-8-9, 30 points), which has lost once in its last 12 matches.
Jack Price picked up his team-leading ninth assist on Wilson's goal for Colorado (12-4-8, 44 points) as the third-place Rapids settled for a fourth consecutive draw and drew within a point of second-place Seattle.
William Yarbrough stopped three shots to preserve the home draw for Colorado, which could be sitting atop the West right now if it had turned two of those four draws into wins.
Wilson put the Rapids in front in the 28th minute when he rose between a pair of defenders to head Price's in-swinging corner kick past Crepeau.
White leveled 12 minutes later on a chance that began with Wilson's errant pass in his own end. Deiber Caicedo intercepted the pass in stride and then sent a throughball into the penalty area. White ran onto it and hammered a powerful finish past Yarbrough.
The second-half chances were fairly even, with substitutes doing the most to test the goalkeepers.
Vancouver's Lucas Cavallini twice forced Yarbrough into two stops after coming on in the 60th minute.
Andre Shinyashiki had Colorado's best opportunity in the 83rd minute on his first touch. He took Younes Namli's slip pass and fired a low shot that forced Crepeau into an excellent diving save to his left.
Another Namli cross found Kellyn Acosta in an excellent position deep into second-half stoppage time, but Acosta's first-time volley landed comfortably into Crepeau's body.