Norrie had lost his four previous meetings against Nadal but produced some of his best tennis at a sold-out Ken Rosewall Arena to give Great Britain a 1-0 lead against Spain at 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.”
Norrie, who defeated Alex de Minaur in his opening match at the new mixed-teams event as Britain beat Australia 3-2, was no match for Nadal in the opening set.
Nadal, making his first appearance since the Nitto ATP Finals in November, delivered a series of stunning passing shots, 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.
Britain’s Katie Swan will bid to put Britain 2-0 up in their Group D tie when she faces Spain’s Nuria Parrizas Diaz in the last match of the day.