The 38-year-old, who was released by QPR in the summer, displayed clinical finishing in front of goal to sweep home a David Bell corner to claim his fifth of the season on the half-hour mark.
And that was added to in spectacular style when the impressive Bell unleashed a left footed drive from 25 yards that was worthy of winning any game.
Port Vale managed a late consolation through Luke Rodgers, but the defeat heaped more pressure on manager Martin Foyle, who now sees his side stuck in the relegation battle.
Vale, who were without a win at Kenilworth Road in 109 years, endured a miserable afternoon and were up against it for most of the game after Ashley Westwood was sent-off with a straight red card late in the first half.
Luton almost made the perfect start to proceedings when Bell floated over a corner on two minutes which was met by Alan Goodall's downward header that zipped off the surface and crashed against the crossbar.
Vale had failed to show any dominance in front of goal, but with their first real attack of the game they almost broke the deadlock.
David McGoldrick was given time on the ball on 26 minutes to turn inside his marker and drill a low shot that flashed wide of David Forde's goal.
But that was as good as it got for the visitors as Luton were soon in front.
Bell was the provider as his corner was swept home by Furlong at the near post, leaving Vale goalkeeper Joe Anyon with no chance.
It got worse for Vale just three minutes before the half-time whistle when they were reduced to ten men.
Not many inside the ground could work out what Westwood was sent off for, but the referee had no hesitations in showing the defender a straight red card - which could only have been for dissent.
After dominating the second half, Luton wrapped up the win in spectacular style when Bell popped up with a thunderbolt shot with just four minutes remaining.
Vale did find a consolation when Rodgers' header from six yards found a way through, but it was far too late from the visitors as Luton held on for all three points.