The scores were locked at 2-2 and 30-30 in the deciding set of Saturday's match when Nadal admitted the ball had struck his body while playing a close-range shot that made it over the net.
Nadal saved the ensuing break point, but world No.14 Norrie snared the break shortly after on the way to wrapping up the 3-6 6-3 6-4 victory in two hours 44 minutes.
The result gave Great Britain a 1-0 lead over Spain in the tie.
Great Britain beat Australia 3-2 in their opening round, and they will top their group if they can beat Spain in the best-of-five tie.
World No.70 Nuria Parrizas Diaz will be aiming to level the tie when she faces off against Katie Swan in the women's singles rubber.
Nadal won the Australian Open and Roland Garros early in 2022 to take his career grand slam tally to 22, but foot, rib and abdomen issues meant he played just four events after Wimbledon in July.
The 36-year-old looked rusty at times against Norrie, and he has just over two weeks to regain his magical touch ahead of his Australian Open defence.
Norrie failed to win a set in his four previous encounters against Nadal and he was thrilled to get the win.
"It was pretty crazy. I was thinking I'd never won a set before, so I wanted to come out and firstly do that," Norrie said during his on-court interview.
"It was a super physical match and I enjoyed it. It's huge to get through that one. He beat me easy the last few times.
"I felt like I was finding really good depth on my shots.
"Tactically, I think it was a pretty good match and I served my way out of some trouble. It's a great way to end 2022 for me."
Although Nadal struggled with his first serves in the opening set and he committed several uncharacteristic shanks, his overall class shone through during the key moments.
Nadal unleashed a forehand winner to snare the crucial break in the sixth game and he saved a break point a short time later on the way to wrapping up the set in 52 minutes.
Norrie started the second set strongly and Nadal was in a hole at 0-40 down on serve in the sixth game.
Nadal saved four break points before a backhand mis-hit handed Norrie the break.
Norrie served out the set, and he was well on his way to victory after securing a break in the fifth game of the third set.
Nadal created a break-point chance in the eighth game but Norrie produced a forehand winner to close the door.
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