Jacobson scored in the 88th minute and Zimmerman followed with his first career MLS goal in the 90th to cap the stunning comeback for Dallas (8-3-5), which remains unbeaten at home this season at 7-0-2.
Dallas remains atop the Western Conference standings, despite winning just once in its last five matches (1-2-2).
After Kei Kamara's penalty kick goal in the 43rd minute and an own goal in the 58th, Kansas City (6-5-5) seemed to be in good shape, even after going down to 10 men following C.J. Sapong's ejection in the 68th minute.
KC goalkeeper Jimmy Nielsen made four saves and appeared ready to earn his eighth shutout of the year.
Dallas nearly won it in stoppage time, but Kenny Cooper's 20-yard blast curled just wide of the right post.
The comeback was started by Ramon Nunez, who entered the game in the 74th minute and was making just his second appearance of the season. Jacobson's header off Nunez's delivery from 15 yards out beat Nielsen over the shoulder, landing in the upper right corner for his third goal of the season.
Dallas kept pressing, and after David Ferreira's free kick from near the right sideline sailed into the penalty area, Zimmerman headed it off Nielsen's hand and in.
The 25-year-old Zimmerman, making just his fourth MLS appearance, entered the match as a halftime replacement for defender Matt Hedges.
Kamara's second goal of the season came in the 43rd minute on a penalty kick.
The PK was set up by a foul called on Jacobson, who grabbed Aurelian Collin's arm as Graham Zusi's free kick sailed into the box. Collin went down and the foul was called, just as Claudio Bieler popped the loose ball into the net. The goal was waved off, but the penalty kick was awarded.
Kamara then stepped up to the dot and drilled a shot into the upper left portion of the net, while Dallas goalkeeper Raul Fernandez dove to the right.
Kansas City's 1-0 lead marked just the second time this season Dallas trailed a game at the half.
Dallas almost tied it in the 55th minute, when Michel's corner kick was re-directed in close by a leaping header from George John, but the ball went just over the crossbar.
Sporting went ahead 2-0 three minutes later when Zusi's corner kick bounced past several players into the penalty area, hit Dallas defender Je-Vaughn Watson in the chest and ricocheted past Fernandez.
FC Dallas continued to press, forcing Nielsen to come up with a big save on Cooper's 15-yard blast from the left wing in the 65th minute.
The complexion of the match changed three minutes later, when Sapong was shown a red card and ejected after kicking the ball at Jacobson's head, who had just been knocked down and was lying on his back.
Dallas didn't really seem to have an advantage with the extra man until the final minutes.