Kansas City had looked on track to bounce back from two straight defeats with a win over 10-man Toronto when in-form striker Dom Dwyer converted a penalty with six minutes left at Sporting Park on Friday.
But in the second minute of second-half stoppage time, Orr stunned the home crowd, getting his head to Nick Hagglund's speculative cross after Sporting had failed to clear Toronto's initial free-kick.
The draw took Toronto to 13 points in the MLS' Eastern Conference and above Columbus Crew to sixth, extending their unbeaten run in all competitions to four games, while Sporting missed the chance to claim top spot in the standings.
Instead, Kansas City rose to second on 18 points, ahead of DC United on goal difference, while New England Revolution (20 points) remain top.
After a goalless first half, Sporting took a deserved lead two minutes into the second period when Dwyer started and finished a move.
The 23-year-old skipped past a couple of Toronto defenders before spraying a pass to Sal Zizzo on the left, who returned it to Dwyer to finish from near the penalty spot with a first-time shot.
Sporting ended the game with 17 shots to Toronto's seven and looked set to cruise to victory when the visitors were reduced to 10 men just after the hour-mark.
Steven Caldwell was sent off for a high boot into Antonio Rodriguez's groin but Toronto dragged themselves back into the contest just four minutes later thanks to Luke Moore's second goal in as many games.
With the advantage of an extra player, the hosts created the better chances to win the match and when Igor Juliao earned a penalty thanks to a clumsy block from Toronto substitute Doneil Henry, Sporting looked on track for victory.
Dwyer slammed home his 10th goal of the season to take the lead in the league's goal-scoring standings but Kansas City had to settle for a point after Orr hit the back of the net for the first time in the MLS.
