Dominique Badji broke the deadlock on five minutes before Joe Mason added a second just three minutes later in Colorado's home opener.
The visitors pulled a goal back through Felipe Gutiérrez just before the hour mark and Rubio fired home in the first minute of additional time to rescue a point for Sporting KC.
Colorado are still winless this season, while Kansas City moved top of the Western Conference after picking up a point in their second road game.
The Rapids' long wait to play in front of a home crowd in Commerce City was over and they made the most of it by breaking the deadlock early in the game.
Badji and Mason hand Colorado an early lead
Jack Price switched the ball across to Édgar Castillo on the left, and the midfielder played the ball across to Badji, who struck home clinically inside the area.
If that didn't lift Colorado's homecoming enough, then three minutes later, the Rapids doubled their lead in the game.
Castillo played the ball back to Tommy Smith, whose long ball over the Kansas City back line was latched upon by Mason and the forward tried to go around the 'keeper at first, but came back and fired home.
Sporting KC came close to pulling a goal back on the stroke of half-time. Yohan Croizet skipped past Smith in the area and his shot was saved well by Tim Howard before Khiry Shelton's rebound was kept out by Colorado's keeper.
Just 37 seconds into the second-half, Kansas City were denied once more by Howard. Shelton played a one-two with Johnny Russell and his low strike was saved superbly by the 'keeper.
Colorado should've gone three-up on 54 minutes after Price's free-kick was flicked on by Smith and Badji miscued his header at the back post from around a yard out.
Gutiérrez pulls a goal back for the visitors
Three minutes later, down at the other end of the field, a cross to the back post was headed down onto the post by Croizet.
However, the Rapids failed to clear the ball and Gutiérrez fired home the rebound into the bottom corner for his fourth goal in as many games this season.
Graham Zusi's corner from the left was swung into the penalty area, Gutiérrez had two chances to strike the ball home, but Howard came out and collected.
Heading into the final stages of the game, Colorado had a chance to seal their victory, but Price's free-kick, on the edge of the area, thundered off the crossbar.
Rubio scores equalizer to earn SKC a point
Sporting KC broke to the other end of the pitch and after Shelton rolled the ball back into the path of the oncoming Rubio, the Chilean calmly slotted the ball past Howard.
Niki Jackson's late strike flew inches over the bar and seconds after that, the match referee drew the game to a close.