It was the first time since 2016 when Andy Murray and Novak Djokovic were battling for the world No1 spot that two players faced each other in finals in back-to-back weeks.
A week previously in Argentina, Alcaraz had dominated and was the favourite to do so again, with victory putting him level on points with world No1 Djokovic in the world order.
The Spaniard looked on course for the win with a set and break up but Norrie fought back brilliantly to seal his fifth ATP Tour title with a 4-6, 6-4, 7-5 victory.
“It’s so special to win this one especially after losing a couple of finals already this year,” said the Briton. “I had to do it the tough way. I was a set and a break down and 0-30 on my serve. I managed to flick a switch and turn it around so it was a good day.
“I had to battle a lot of demons in the last couple of weeks but managed to play well in the big moments and that’s what it took today.
“The match could have gone either way but I managed to run a little bit more and it was a really good match. It’s an honour to share a court with you again and compete with you.”
Victory moved Norrie up to 12th in the world in the revised rankings on Monday, while Murray catapulted himself up 18 places to 52nd following his Qatar Open final appearance on what was a good weekend for British tennis.
Norrie and Alcaraz could barely be separated during an engaging match. The British No1 had chances to break in the opening set at 2-2 only for Alcaraz to hold and then break himself to take that first set.
Norrie was again left to rue his missed opportunities in set two as he let two break points go begging on the opening Alcaraz service game. It proved something of a theme as Norrie converted just 6 of 16 break point opportunities in contrast to his opponent’s five from nine.
But crucially they came when it mattered as Norrie faced a second successive final defeat after an early break to fall 3-0 down. He then won four games in a row before being broken only to break again and force a deciding set.
In the decider, the breaks of serve kept on coming in that final set, telling Norrie getting the last of them to give him a 6-5 lead. He then sealed the match with an ace to beat last year’s Rio champion, who appeared to be struggling with a leg injury as the match reached its conclusion on the clay.