Norrie is expected to climb to ninth in the world rankings despite his defeatBritish number one Cameron Norrie lost to Croatian Borna Coric in straight sets in the semi-finals in Cincinnati.
Coric reached his first ATP Masters 1000 final since shoulder surgery last year, outplaying Norrie throughout as he won 6-3 6-4 in just over 90 minutes.
He will meet Stefanos Tsitsipas in the final, after the Greek overcame Russia's world number one Daniil Medvedev 7-6 (8-6) 3-6 6-3.
"It was a very tough day," said Coric, ranked 152nd in the world.
Both semi-finals were delayed by rain and Coric added: "At the beginning I was not there, I was not feeling the ball very well. Then I did find my rhythm. I started to serve better, I started to play much better and I think that was the key to the match."
Norrie raced into a 3-1 lead before Coric reeled off five straight games to take the first set.
He maintained the pressure into the second set, winning eight straight points to race into a 4-2 lead before claiming victory.
Coric, who beat Rafael Nadal earlier in the tournament, will now face a third career meeting with world number seven Tsitsipas and could improve his ranking to as high as 29th with victory.
Fourth seed Tsitsipas saved a set point in the opening tie-break and won the final three points to take the first set, but then fell to 5-0 down in the second.
He managed to recover and took the momentum into the third, breaking the US Open champion at 3-2 and serving out the match comfortably to record just his third win in 10 against Medvedev.
The US Open, the final grand slam of the year, starts on 29 August.
Kvitova to face Garcia after dispatching Keys
Two-time Wimbledon champion Petra Kvitova will face French outsider Caroline Garcia in the final after coming from a set down against American Madison Keys to win 6-7 (6-8) 6-4 6-3.
Kvitova's recovery surged in the third set when she broke Keys in the opening game.
The Czech narrowly avoided being pegged back at 4-3, regaining control to hold her serve from 40-0 down before breaking again for the win.
World number 35 Garcia became the first ever qualifier to reach a WTA 1000 final after a 6-2 4-6 6-1 win over world number seven Aryna Sabalenka of Belarus.
Garcia was dominant in the opening set, striking 13 winners and converting two break points before the rain came at 1-1 in the second. It was then that Sabalenka came roaring back, breaking three times to take the set.
Another stoppage, this time a medical timeout for Garcia, was followed by a second rain delay, but she regained her form to break twice in the decider and set up a clash with Kvitova.
"I guess no-one expected it, that's for sure," Garcia said. "It's a long way to come from qualifiers."
