Jay Heaps' men came from behind twice in front of their home fans at Gillette Stadium to earn a 4-3 aggregate victory.
Charlie Davies was the hero, first cancelling out Tim Cahill's opener before responding to Peguy Luyindula's goal.
The Revolution are four-time MLS Cup runners-up, but will get their chance once more against either the Los Angeles Galaxy or Seattle Sounders.
Cahill put the visitors ahead in the 26th minute, getting on the end of Thierry Henry's well-weighted pass before scrambling in from close range.
The equaliser, which came four minutes before the break, was also scrappy.
Chris Tierney's short corner led to a cross and Davies, in a crowded penalty area, saw an attempted header come off his shoulder and find the bottom corner.
But the tie was level in the 53rd minute thanks to Luyindula.
Cahill jumped for Lloyd Sam's hopeful ball into the area and the Australian's presence led to an error, allowing Luyindula to fire in from close range.
There would be no way back for the Red Bulls when Davies and Tierney combined again in the 70th minute.
Tierney's cross from the left found Davies in the area and the 28-year-old American headed in to send the Revolution into the final.
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