An incandescent Houston was sent to the stand after 56 minutes following an robust tete-a-tete with referee Barry Cook.
The Bairns were already trailing 2-1 at that point after Iain Davidson and Mark Stewart goals cancelled out a John Baird equaliser.
Houston’s frustrations were exacerbated by the sight of Declan McManus and Stewart adding further goals for the visitors after Lee Miller briefly brought the score back to 3-2.
It was a productive afternoon’s work for Gary Locke’s Raith side, who leap-frog Falkirk into fourth in the Championship on goal difference. Their performance wasn’t easy on at the eye at times but they were ruthless in the final third.
“Not one player got up to the standard that we set,” lamented Houston. “I’m absolutely shocked – I didn’t see it coming.”
It turns out Houston was sent to the stand for urging the referee to stop time-wasting.
“He came over to Gary and I stood behind him and heard him explain his decision to book Kyle Benedictus. If you get every referee explaining every decision, the game won’t be 90 minutes long. I just told him to get on with the game.”
Raith’s bright start set the tone for a fruitful afternoon, Bairns keeper Danny Rogers making saves to deny Stewart, who made his first league start of the season, and Benedictus.
The visitors went ahead in the 17th minute when Davidson turned in a close range strike after Jordan Thompson’s corner was not dealt with.
That advantage was obliterated a minute later as the away side shot themselves in the foot.
A communication breakdown between goalkeeper Kevin Cuthbert and defender Jean-Yves Mvoto allowed Baird to latch on to Mark Kerr’s pass and the striker kept his cool to roll the ball into the net.
After a Bob McHugh goal was ruled out for a foul in the build up, Falkirk should have taken the lead but Mark Kerr shot wide with only Davidson guarding the goal.
That thriftlessness came back to haunt Houston’s side as Rovers regained the lead in the 37th minute. Bobby Barr’s low pass into the area caused problems and after Ross Matthews’ header was only partially saved by Rogers, Stewart nodded the rebound into the unguarded net.
McManus added a third for Raith in the 72nd minute with a simple tap in from close range after connecting with Stewart’s low cross but Falkirk responded when substitute Miller nodded in Scott Shepherd’s header back across goal.
Stewart secured the win in the 79th minute when he took advantage of a David McCracken error to round Rogers and find the empty net.
“I’m over the moon,” said Raith manager Locke. “I felt that’s the best we’ve played. To come here and get a result like that you have to play well and we certainly did that.”