After a rare rain delay halted play in the match's early stages, Tiafoe whipped a forehand crosscourt winner to break Norrie for a 4-3 lead.
The dynamic Tiafoe, who fed off the energy of the supportive crowd, then pressured Norrie into an error on set point by coming into the net.
Tiafoe saw his double break second-set lead whittled down to one when he double-faulted at 5-3.
But he managed to serve out the match on his next opportunity, unleashing a 139 mph ace to set up match point before ending the affair when Norrie's forehand sailed long.
The loss snapped Norrie's eight-match winning streak. The tournament's 10th seed won the title in Rio de Janeiro last month and has a 21-4 win-loss record for the year.
"I truly feel like when I'm there mentally, I'm one of the best players in the world," Tiafoe said.
"Today it is not just about getting to the semis, I am happy to beat a guy like that, who has been playing so well.
"To be able to come out here and beat him in straight sets, relatively comfortable. At the end, it got a little tricky, but it was pretty much one-way traffic and I am really happy with where my game is at."
Tiafoe, who has yet to drop a set at the tournament in the Southern California desert, reached the semis of last year's US Open where he fell to eventual champion Carlos Alcaraz (19).
Tiafoe will have his work cut out for him on Saturday when he faces the fifth-seeded Medvedev, who extended his winning streak to 18 matches with his victory over Davidovich Fokina in the breezy afternoon session.
Medvedev raced out to a 3-0 first set lead and crushed an ace to capture the opener as Davidovich Fokina searched for answers.
In the more competitive second set Medvedev, who had injured his ankle in his previous match, required attention from a trainer to tape his bloody right thumb but the bandage did not hinder his shotmaking.
His speedy defense helped him break Davidovich Fokina at love for a 6-5 lead and he smacked an unreturnable serve on match point in the next game to keep his hopes of a fourth consecutive title alive.
Medvedev is 4-0 against U.S. Open semifinalist Tiafoe but they have not faced each other since the 2021 Miami Open.
"He's playing great," Medvedev said of Tiafoe.
"Frances is a very pumped up, fire player, so he can beat anyone on a good day. I'm sure he can beat Novak (Djokovic), Rafa (Nadal). He actually did beat Rafa at the US Open, which is huge.
"I need to try my best to keep this head-to-head at zero. That's never easy but I just have to show my best tennis and try to beat such a great opponent."
