The first real chance of the match came for the hosts. With 11 minutes on the clock winger Jai Quitongo broke free from a long ball and rounded goalkeeper Morrison.
However, Brad McKay cleared his low effort off the line to keep the score level.
Former Falkirk man Jaze Kabia then had a shot from range arrow wide of target.
John McGlynn’s side were lacking a creative spark and they failed to create a real chance before the half time break.
Quitongo was sent off for a high tackle on Liam Henderson just before the interval to reduce Morton to ten men.
Mackie created the first moment of quality for the Bairns, lofting a ball into the path of Craig McGuffie who fired a header over from a central position.
On 55 minutes, debutant Henderson then saw red for hauling down Kabia one-on-one, leaving both sides with ten men on the pitch.
Moments after McKay saw an acrobatic effort in the area just go over the bar.
Mackie was the next to have another shot at goal, this time smashing a long range drive off the bar on 70 minutes.
Falkirk could have been done to nine men when McKay brought down substitute Lewis McGregor - who was darting past the Bairns backline when he taken out.
A downward header from Reece Lyon then should have put Morton ahead.
The midfielder broke into the box and saw his effort hit the crossbar with Morrison scrambling.
On 75 minutes ex-Bairn Cameron Blues then shot wide in the box when it looked easier to hit the target.
In the final seconds of the match Jaime Wilson looked like he could grab a winner when some neat play saw him played in on goal but a last-ditch challenge ensured spot-kicks.
With the shoot-out level at 4-4, Kabia’s attempt to fool Morrison cost his team an extra point as his weak effort down the middle was saved.
McKay then stepped up and scored the important spot kick to give Falkirk two points to take home from Greenock.