The visitors fought back from 1-0 behind to land the three points while Livingston finished with 10 men after Iain Russell received a second yellow card.
Falkirk created the first good chance but David Weatherston's effort came back off the post.
The hosts then began to cause problems and they took the lead when Russell converted a penalty on 26 minutes after Darren Dods was ruled to have fouled Daniel Mullen.
But Falkirk made it 1-1 in the 62nd minute when Dods crossed and Sean Higgins was on hand to convert the chance.
And the Bairns then got the winner 11 minutes later, when Livingston's Jason Talbot put Thomas Grant's cross into his own net.
Livingston's ultimately disappointing evening then went further downhill when Russell was dismissed after getting a second booking for a foul on Kieran Duffie.