With time running out in the 91st minute, Olave corralled Jonny Steele's cross, steadied it with a right foot and propelled it into the net, earning a standings point for the Eastern Conference-leading Red Bulls (7-4-4).
Thierry Henry also scored for New York, which ran its unbeaten streak to seven games.
Dominic Oduro and Federico Higuain each notched goals for the Crew (4-4-4), who remained in sixth place in the East.
Disney's 'Jessie' to feature network's first engagement
Chipotle plans first price increase in 3 years