But the Bairns were indebted to the generosity of St Mirren keeper Mark Howard for their win as the stand-in keeper gifted the home side two goals.
John Hughes will wish St Mirren were the opposition every week as their last encounter at Love Street saw Falkirk triumph 5-1.
It was St Mirren who threatened first when Andy Dorman fired a 20-yarder wide but Falkirk burst into the lead after only seven minutes.
Carl Finnigan beat Ian Maxwell down the right and supplied a perfect cross for Arfield to bullet in a header off the underside of the bar.
And the home side almost increased their advantage as Darren Barr flicked Pedro Moutinho's corner goalward, but Stephen McGinn was stationed on the post to clear the danger.
The visitors should have levelled after 22 minutes when Dorman ran on to Craig Dargo's clever flick only to put his right-foot shot wide of the target.
But Saints were having their best spell and Maxwell's deep cross was volleyed wide by Hugh Murray at the back post.
And Dorman was the sinner again in front of goal as he let Billy Mehmet's pass run away from him before slicing his shot wide as he overstretched.
After the break Saints had another chance to level when Mehmet's header fell to Murray, but he was just too high with a powerful right-foot drive from 20 yards.
St Mirren paid the price for their poor finishing as Falkirk finished them off with two goals in four minutes and both were disasters for Mark Howard.
The Saints keeper allowed Arfield's tame right-foot shot to bounce off his arm, through his legs and into the net for Falkirk's second.
And then the keeper came charging off his line and attempted to punch clear Jack Ross' long free-kick. However, he only succeeded in knocking the ball to Cregg, who headed back over the prostrate keeper into the empty net.
Cregg added his second goal after 71 minutes with a glorious left-foot strike from 20 yards to round off the scoring.