The world number 13 had lost all of his previous four meetings with Nadal in straight sets, but delivered for Great Britain in the inaugural mixed international team competition.
The 27-year-old said in his post-match interview: “It was pretty crazy. I was thinking I’d never won a set before (against Nadal) and I came out firstly wanting to do that.
“I had to stay super-patient. It was a super-physical match and I enjoyed it. It was huge to get through that one and finally beat him.
“He bet me easily the last few times, so it’s a great way to end the year for me. It was a crazy atmosphere, thank you guys. It was a crazy match.”
Nadal, making his first appearance since the Nitto ATP Finals in November, delivered a series of stunning passing shots in the opening set, but was unable to maintain his level.
Norrie broke the Spaniard in the sixth game of the second set and went on to dominate the decider, saving two break points while leading 3-2 before holding his nerve to clinch a statement win.
Speaking after the match, Nadal was in no mood to discuss his longer-term tennis future.
“When the day arrives that I go out on court and say ‘that’s getting hard’, is the day to say goodbye. I don’t want to and I don’t need to keep playing for no one reason,” Nadal said.
“The only reason that makes sense to keep playing is if I really enjoy what I do and if I really feel it. If I don’t feel it, I mean, I did much more than what I ever dreamed.”
Nadal added: “But either way, for me, I lost my match. That’s it, no? Every time that I am coming to a press conference seems that I have to retire.
“So you are very, very interested on my retirement? That is for the moment, not the case.
“When this day arrives, I’m going to let you know. Don’t keep going with the retirement (questions) because I am here to keep playing tennis.”
Katie Swan produced a superb fightback to beat Nuria Parrizas Diaz and keep Great Britain in control of the United Cup clash after Norrie’s win.
Ranked 145 in the world, Swan produced a fine display as she recovered in her match against Parrizas Diaz after the Spaniard had taken the first set.
Encouraged by team captain Tim Henman, the 23-year-old rallied to defeat the world number 70, coming through 3-6 6-1 6-2 for her first win in the competition.
Spain will now need to mount a recovery of their own in Sunday’s fixtures to stay alive in the tie, while victory will see Britain qualify for the quarter-finals.
Paula Badosa, the world number 13, will take on Harriet Dart, who beat her at the Billie Jean King Cup, while Pablo Carreno Busta faces British number two Dan Evans.
Should the tie end up level at 2-2 after the singles, it will be decided on mixed doubles, which would see Nadal and Badosa play Evans and Dart.
Additional reporting by PA Sport.