The 26-year-old Muller, ranked 84th, has spent most of his professional career on the second-tier challenger circuit.
At key moments U.S. Open champion Alcaraz produced backhands that swerved round the net post, lobs that puffed the baseline chalk, and unreturnable serves that reached 130 miles an hour.
After breaking serve in the seventh game, Alcaraz won the first set on his fourth set point with a big serve the Frenchman could not deal with.
"I'm getting more experience and getting better every game," Alcaraz said in an on-court interview.
Reporting by Clare Lovell, editing by Ed OsmondOur Standards: The Thomson Reuters Trust Principles.
Persons:
Spain’s Carlos Alcaraz, France’s Alexandre Muller, Andrew Couldridge, Carlos Alcaraz, France's Alexandre Muller, Muller, Alcaraz, unreturnable, I'm, Clare Lovell, Ed Osmond
Organizations:
Lawn Tennis, Croquet Club, France’s Alexandre Muller REUTERS, Wimbledon, Frenchman, Thomson
Locations:
London, Britain