New England will head to the Midwest with a slim advantage, thanks to Andy Dorman and Kelyn Rowe.
The first half was a scoreless occasion, although the visitors came closer to breaking the deadlock. Teal Bunbury came close to opening the scoring in the 17th minute, but his effort at the near post off Jacob Petersen's cross was just wide, and Aurelien Collin would have scored on the ensuing corner kick but for the chest of Lee Nguyen.
Bunbury had another close chance in the 35th, latching onto a long ball out of the back for a one-on-one with Matt Reis, but the veteran keeper stood his ground and saved the forward's shot.
With the prospect of a scoreless result heading into a deciding game in Kansas, New England shifted to open the second half, pushing Dmitriy Imbongo higher into a closer approximation of a 4-4-2.
The gamble paid off as the Revolution took the lead early in the second half. Matt Reis saved Diego Fagundez's shot from a wide area, but only pushed it into Juan Agudelo, who played it ahead for Andy Dorman to tap in.
Kelyn Rowe made it 2-0 in the 67th. Coming in from a wide right position, Rowe got just enough on a pass dished out by Nguyen to pick out the low far corner.
Kansas City pulled one back almost immediately. In the aftermath of a long Graham Zusi free kick, Chance Myers lined up a panicked shot that was headed wide before a flick from Lawrence Olum put the ball in a perfect position for Collin to tap home.
Kansas City will host the return leg on Wednesday, Nov. 6 at Sporting Park.