The Rapids looked to have secured a point when Jonathan Lewis equalised with six minutes of normal time remaining after Diego Rubio and Jack Price had been sent off in Orlando, Florida on Saturday (AEST).
But Zusi's deflected shot in stoppage-time ensured Sporting KC snatched all three points in a dramatic Group D clash at Walt Disney World resort.
Colorado led through Kellyn Acosta's sixth-minute opener and it was not until the 65th minute that Sporting KC restored parity courtesy of Khiry Shelton from an acute angle.
Rapids forward Rubio was ruled to have handled Zusi's cross inside the box and sent off after a VAR (video assistant referee) review seven minutes later, and Alan Pulido converted the penalty.
After Colorado's Price was shown a straight red card for dissent moments later, Lewis found the far corner of the net to make it 2-2 in the 84th minute but Zusi's long-range attempt took a wicked deflection and looped over Rapids goalkeeper William Yarbrough in the second of 12 additional minutes.
It was Sporting KC's first win after two fixtures as it improved to three points, one point adrift of Real Salt Lake and Minnesota United.
RSL and Minnesota both had the chance to reach the last 16, however, the Western Conference foes played out a 0-0 draw.
Meanwhile, DC United salvaged a 1-1 draw against New England Revolution in Group C.
Federico Higuain, the brother of Juventus forward Gonzalo, came off the bench and rescued a point with 18 minutes remaining following Adam Buksa's opener six minutes into the second half.
DC is still searching for its first win after back-to-back draws, while Revolution is level with Toronto on four points.