Bou scored the tying goal on a penalty kick and added the go-ahead tally in transition for the Revolution (15-9-10, 55 points), who won for just the second time under interim coach Clint Peay.
The Union (15-9-10, 55 points) slipped from third to fourth place on Decision Day with the loss, coupled with the Columbus Crew's victory over CF Montreal.
But Philadelphia held on to a top-four playoff seed despite posting an identical record to New England, thanks to the goal-differential tiebreaker. The Union will have home-field advantage for a best-of-three, first-round playoff series with the Revolution.
The Union opened the scoring in the 16th minute.
Philadelphia cleared the ball upfield toward New England's box, with two Union players closing in. Revs defender Dave Romney tried to head it out of the way, but Jackson also dove and partially batted the ball, leaving it behind him in the box. Carranza had gone to the ground and kicked it in lying on his side.
Union defender Damion Lowe was called for a handball in the 23rd minute when a shot attempt hit him in the left elbow. Two minutes later, Bou deposited his penalty kick in the bottom-left corner of the net.
The Revolution then seized the lead on a fast break in the 41st minute. Carles Gil sent a centering pass to Bou, who beat Blake at the near post for his seventh goal of the season. He hadn't scored in a regular-season match since July 15 after missing time with a leg injury.
Tomas Chancalay had a few chances for New England around the 70th minute but couldn't convert.
The Union's Kai Wagner had a free kick in the 87th minute and Nathan Harriel got on the receiving end for a one-time goal that would have tied the game, but Carranza was whistled offside to nullify it.