Murray, the tournament's second seed, took advantage of the top seed's right knee injury after splitting the first two sets 6-3, 4-6.
The 21-year-old Scot showed no ill effects from his own ankle injury, sustained during his quarterfinal win over France's Marc Gicquel.
In the rubber set, Murray grabbed a 2-0 lead after a quick service break and the rout was on.
"Obviously it's not the way you want to win as I could see Rafa had an injury," Murray said. "He made it difficult as he was hitting the ball so hard and being aggressive on every shot to try and keep the points short. This has to count as one of my biggest victories."
Murray took home a $356,000 winner's check and his career record in finals rose to 10-5.
Nadal was denied a 33rd career title.
Celebrity Families of 2014 [PHOTOS]