The Fire entered their ninth match of the campaign winless, while the Red Bulls were unbeaten at home in four matches so far at the Red Bull Arena.
However, all that changed when the Fire - leading 5-2 at one stage - held on for a famous 5-4 victory.
Harrison Shipp had given the visitors a fourth-minute lead in controversial circumstances, despite Mike Magee seemingly in the play and in an offside position.
The response from the Red Bulls was sharp, with Australia international Tim Cahill - notably infuriated with the non-offside call - nodding in the equaliser two minutes later.
Bradley Wright-Phillips put the Red Bulls in front six minutes out from half-time, but from there, the Fire would take control.
Quincy Amirakwa snuck in behind, and flicked a header into the back of the net for 2-2 early in the second half, before Shipp scored twice in the space of five minutes to complete his hat-trick and all but seal the result for Chicago.
Patrick Nyarko made it 5-2 on 64 minutes, with a cross-cum-shot more salt into the Red Bulls' wounds, however they would not give up without a fight.
Wright-Phillips smashed his second goal of the night home from the edge of the area, before converting a 78th-minute penalty for his hat-trick, and ensuring a nervous finish for the Fire.
But the visitors held on for the three points, to open their winning account in dramatic fashion.
Eastern Conference leaders Sporting KC are three points clear, after a 3-0 thrashing away to cellar-dwellers Montreal Impact.
Dom Dwyer's brace sandwiched Paulo Nagamura's effort, with Montreal's fate virtually sealed by the dismissal of Collen Warner on 17 minutes.
DC United climbed above Red Bulls into second in the East, with a 1-0 win at Philadelphia Union.
Chris Rolfe's sixth-minute strike was all DC required for their fourth win in nine.
Vancouver Whitecaps made it four wins from all four visiting sides on Saturday, with a 1-0 win at Columbus Crew.
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