The 22-times Grand Slam champion, who lifted the trophy in Melbourne Park this year and added another French Open title in an otherwise injury-ravaged season, eased through the first set but gifted Norrie a way back into the contest in the next.
Nadal dug himself out of a hole with an ace to hold for 2-1 in the decider but surrendered his serve shortly after as world number 14 Norrie got sharper as the contest wore on and held on for the first win over the world number two in five attempts.
"It was pretty crazy... I was thinking I've never won a set against him before and I wanted to come out and firstly do that and I had to stay super patient," Norrie said in his on-court interview. "It was a super physical match.
"I really enjoyed it, it was huge to get through that one and finally beat him. It's a great way to end the year."
Norrie credited his pre-season training for being able to dictate the baseline exchanges at Ken Rosewall Arena.
"I've had a really good off-season, played a lot of matches and it's been good for me. I felt like I was finding really good depth in my shots and dictated the play... I wasn't letting him do too much damage with his forehand," Norrie added.
Katie Swan (23) then doubled Britain's advantage as she rallied from a set down to get past Nuria Parrizas Diaz (31) 3-6 6-1 6-2.
Women's world number one Iga Swiatek (21) had no trouble in her season opener as she dismantled Yulia Putintseva (27) 6-1 6-3 to give Poland a 1-0 lead over Kazakhstan in Brisbane.
Earlier, Czech Republic's Jiri Lehecka (21) claimed the biggest win of his career by stunning world number 12 Alexander Zverev (25) 6-4 6-2, before Marie Bouzkova (24) beat Jule Niemeier (23) 6-2 7-5 to give her team a 2-0 lead over Germany.
Playing in his first competitive match since surgery to fix his ankle ligaments following an injury at Roland Garros, Zverev looked short of fitness and struggled on his serve with eight double faults to go down.
Brazil took a 2-0 lead over Norway as Beatriz Haddad Maia (26) and Felipe Meligeni Alves (24) both prevailed while Donna Vekic (26) and Borna Coric (26) put Croatia 2-0 up against Argentina. Belgium and Bulgaria were locked at 1-1. The ties resume on Sunday.
