The 26-year-old reached the last four at a Masters event for the first time in his career, ensuring he will become the new top-ranked British player when the rankings are updated on Monday.
Against a strangely sub-par Schwartzman, Norrie again proved irresistible on the California hard courts.
He won the first set without losing a game in 31 minutes.
The fluid left-hander followed the set flawlessly with a largely comfortable second, beating his Argentinian opponent three times, to advance to the semi-finals.
Norrie will meet either Gregor Dimitrov or Hubert Hurkacz for a place in the final.
His victory secures him a place in the world top 20 for the first time, taking him past current British number one Dan Evans, whom Schwartzman beat earlier in the week at Indian Wells.
Norrie becomes the 18th man to lead all Britons in the ATP rankings since their inception in 1973.