The 28-year-old's usually-impeccable forehand was malfunctioning badly and he survived break points in games three and five before more mistakes and a netcord saw him hand Falla a chance to serve for the set at 6-5.
But Spanish ace Nadal kept battling and got a lucky break in the fourth game of the decider as his U.S opponent's return hit the netcord and bounced back on his side of the net to fall down a break.
The tennis gods appeared still to be with the Croatian when a net-cord gave him three set points and he duly converted the second, to the delight of the SW19 crowd.