Rafa De Vita struck an extra-time winner as Livingston beat Championship rivals Falkirk 2-1 in the Betfred Cup. De Vita bundled home from close range in front of a 2,677 crowd which was boosted by Falkirk's offer of free entry to pupils who had received their exam results earlier in the day.Myles Hippolyte and Nathan Austin went close as Falkirk made the early running but Scott Robinson gave Livingston the lead on the break in the 31st minute when he turned home Danny Mullen's cross from close range.The lead only lasted eight minutes before James Craigen turned and finished inside the box.Joe McKee hit the Livi bar with a free-kick and both Neil Alexander and Robbie Thomson pulled off excellent saves just before the 90 minutes were up.Former Ross County wide player De Vita struck 11 minutes into extra-time when he converted Josh Mullin's deflected cross.ends