Second-half strikes from Chad Marshall and Dominic Oduro gave the Crew life in the Eastern Conference playoff hunt.
MLS goalscoring leader Marco Di Vaio gave his side the lead in the first half, knifing his way between two defenders to head home for his 18th goal of the season.
The visitors struck back in the second half, however. Chad Marshall grabbed the equalizer with a towering header off a Federico Higuain free kick, before Higuain again turned provider, flicking a through ball on for Dominic Oduro, who scored the winner with a deft touch.
The Impact lost ground in the Supporters' Shield race, while the Crew picked up a crucial win in their playoff chase, as the team now sits just two points out of the final spot in the Eastern Conference.