Falkirk captain David McCracken nodded his side into the play-off positions in a nervy victory.
The Bairns never quite made sure of the victory but saw it out nonetheless to leapfrog Queen of the South.
The match - a second with the Blue Brazil in seven days - was brought forward to allow Falkirk to play their semi-final with Hibs.
But the Bairns will have to play a lot better in that match - and the intervening games than they did against Cowdenbeath.
It was not a night for the purists nor was it a night for shorts and t-shirt, but for Peter Houston, three points was the main objective and that was achieved.
“We have players not on top form and ran the ball out of play under very little pressure six times in the first half,” said the manager in a succinct summation of the first half.
The Bairns had the ball in the net from John Baird after Taylor Morgan shot was blocked but he was flagged offside. Will Vaulks also gave Robbie Thomson a scare by flashing a shot right across goal and inches wide of the far post.
But the goal came moments before the break when David McCracken looped a backwards header over Thomson and into the net from Alex Cooper’s free-kick cross.
The Bairns were not quite clicking, in any position, with Will Vaulks filling in at right-back to cover for Kieran Duffie’s injury and Taylor Morgan still in the side at the expense of Rory Loy but once the striker was replaced by David Smith a sense of urgency briefly burst into the Bairns’ play.
However it couldn’t add to the Falkirk tally and Oyenuga hammered a shot that Jamie MacDonald had to be quick to palm away at the other end.
John Baird had a late chance that zipped past the post but all in all Falkirk’s final pass was poor and possession sloppy.
“The result is the main thing,” added Houston, “but I would like us to entertain. But it’s difficult with so many injuries mounting up through the squad.”
Falkirk play Raith Rovers on Saturday.