Ugandan defender Bevis Mugabi was shown a straight red as the referee pointed to the spot for the second time with seconds left on the clock to allow Doherty to take the game between Motherwell and Coleraine into extra time.
Mugabi was judged to have pulled back Eoin Bradley in the 90th minute, and Doherty calmly sent Carson the wrong way to level the tie.
Goals from Callum Lang and Tony Watt had put the Scottish side in pole position in the first half, but two controversial penalties gifted Coleraine a rare come back.
However, it was Carson’s heroics in the shoot-out that, saving three penalties, that secured a third round clash with Hapoel Be’er Sheva.
The Northern Ireland international Carson spared an Euro humiliation for his side by saving penalties from Parkhill, Kane and McConaghie for a 3-0 win.