With New England's 2-1 loss to Chicago on Sunday, The Union (11-13-9) needed only a tie to secure the final playoff spot.
Philadelphia maintained its three-point lead over New England in the standings and will host the East-leading New York Red Bulls on the final weekend of the regular season next Sunday. The Revolution host the Montreal Impact.
Rivas opened the scoring for Orlando (8-11-14) on a breakaway in the 59th minute. He collided with Union goalkeeper Andre Blake, who came off his line to challenge, and the ball caromed forward into the goal.
Baptista scored on another breakaway in the fifth minute of second-half, stoppage-time with his shot slipping through Blake's deflection.
Orlando City entered the match out of playoff contention.