The 26-year-old won 3-6 6-4 6-1 in an hour and 49 minutes, recovering after being down a break at 3-1 in the second set to secure his second career title in his finest year on the circuit.
Norrie, who started the week ranked 26th, is now guaranteed a top-20 position and has become Britain’s new No 1.
He was the first British player to reach the final at one of the ATP’s nine elite Masters 1000 events since Andy Murray triumphed in Paris in 2016 and is becoming a similarly formidable presence on the circuit as the Scottish former world No 1 once was.
“It means so much to me, my biggest title. I’m so happy, I can’t even describe it right now. It’s absolutely massive for me and my team. I can’t really believe it,” he said in his on-court interview after the match.
Norrie’s success caps a break-out year. Not only has he won Indian Wells and taken his first title, also on hardcourts, at Los Cabos, Mexico, in July, he has made six finals in all - a feat matched only by world number on Novak Djokovic.
The Briton reached four other finals on three different surfaces - on the hardcourts of San Diego, the grass of Queen’s, and on clay in Lyon and Estoril.
“I’ve been really enjoying my tennis and really been enjoying being out on court and competing in the big moments,” he said.
“I’m just really pleased with how I handled the occasion, and I think I’m doing that a lot better this year. I know I lost in a lot of finals so it’s nice to get the big one today.”
Norrie began well by breaking Basilashvili to 15 in the third game of the match and led 3-1 after holding, but later began to struggle in the face of the Georgian’s powerful play.
Basilashvili broke back to draw level at 3-3, and after holding serve broke again for a 5-3 lead before holding serve to love for the set.
The 29-year-old looked in command after sealing an early break in the second set then while serving for a 3-1 lead was broken back by Norrie on a second break point.
As both men dug in, games went to serve from there until Norrie suddenly went up a gear in games nine and 10, holding serve to love then breaking Basilashvili to love to level the match by taking the last eight points of the set.
Norrie took the momentum into the final set, serving his first ace of the match to comfortably hold serve in the first game, then breaking Basilashvili to 30 as more errors crept into his tiring opponent’s game.
Serving to go 3-0 up, Norrie slipped up with his second double fault of the match to go down 0-30 then faced three break-back points at 0-40, but doggedly fought back to deuce through three long rallies, before holding serve after Basilashvili twice hit long.
Basilashvili appeared to be tiring, having to dig deep to hold serve from deuce for 3-1, before Norrie held to 30 on yet another long backhand from the Georgian for 4-1. That became 5-1 when Basilashvili put a forehand horribly wide to be broken to 15, before Norrie held to 15 for the match.
“I was a little bit uncomfortable (early),” said Norrie. “It was quite windy. For a stage he went through and hit so many winners. It was tough for me to get some confidence. The rallies were really short and he was just blasting winners.
“But when I made a couple of big shots in the 5-4 game in the second set it gave me a lot of confidence, and I was able to find my feet again, start moving again, and make the rallies physical like I’ve been doing all tournament and it worked in my favour.”
Basilashvili struck far more winners than Norrie - 23 to 10 - but suffered in making 44 unforced errors to 23 from the Briton, who converted five of eight break points compared with his rival’s three from six.
Norrie said before the final he hoped his impressive run this week would be a springboard for going deeper into grand slams next year, having never made it into the second week of one of the big four tournaments.
This year he suffered third round losses to Rafael Nadal at this year’s Australian and French opens, and to Roger Federer at Wimbledon.