The home side had a decent chance to take the lead in the fourth minute when they won a free kick just outside the box. Dominic Dwyer drilled an effort at goal from the set piece that went just wide of the target.
The Revolution doubled their lead with an individual goal from Jose Goncalves as he won the ball deep in his own half and ran the length of the field before burying a shot into the bottom corner.
Chris Tierney almost added a third for the visitors before the break when he fired a free kick at goal which bounced just before Kronberg, but the keeper managed to palm the ball past the post.
In the second half, Kansas City mustered a response as they got a goal back when Paulo Nagamura collected the ball down the right and raided into the box before placing the ball past Bobby Shuttleworth.
The home side were level a minute later as Toni DiVale's cross to the back post was well kept in by Nagamura, who floated a header across the face of goal, and Dwyer was on hand to head the ball into the empty net.
Graham Zusi had the chance to fire his side ahead when he powered a shot at goal from the edge of the area, but his effort was well saved by Shuttleworth.
The match looked to be ending in a draw until Jones collected the ball 30 yards from goal and drilled a shot into the bottom corner past Kronberg, for his first strike in the MLS, to earn his side the victory.