Benny Feilhaber opened the scoring with a long-range strike after 33 minutes but an own goal from Matt Besler in the 77th minute appeared to sealed a point for the Rapids.
Zusi struck late on, though, latching on to CJ Sapong's pass inside the area to drive the ball home.
The result left Sporting level on 42 points with the New York Red Bulls and the Montreal Impact but top on goal difference.
The Red Bulls got goals from Lloyd Sam (8) and Tim Cahill (38) as they beat DC United 2-1.
Nick DeLeon (36) levelled briefly for United, who could not take advantage when Ibrahim Sekagya saw red for New York in the 73rd minute.
Montreal were held to a goalless draw at the Philadelphia Union.
Robbie Keane scored twice as the Los Angeles Galaxy kept up the pressure on Real Salt Lake at the top of the West.
Landon Donovan celebrated his new contract with the Galaxy with a 26th-minute goal, before Keane scored a penalty just before half-time and rounded off the scoring at the midway point of the second half with a volley from inside the area, taking his tally for the season to 12.
The Seattle Sounders won 1-0 at the Columbus Crew despite playing 83 minutes with 10 men.
Leonardo Gonzalez was dismissed for a professional foul in the seventh minute but Eddie Johnson headed the Sounders ahead eight minutes later and that proved to be the only goal.