The Spanish top seed, who reached the last 16 last year, is attempting to become the third-youngest player in the Open Era to win the title after Boris Becker and Bjorn Borg.
The 20-year-old, seen as the greatest threat to defending champion Novak Djokovic, won his opening match against French veteran Jeremy Chardy on Tuesday.
But heavy rain has played havoc with the schedule at the All England Club -- Djokovic, in action later Friday against Stan Wawrinka, is a round ahead of his rival.
A single break was enough for Alcaraz to seal the first set and he won the second-set tie-break to take an iron grip on the contest.
He broke 84th-ranked Muller again in the eighth game of the third set and served out for the match.
The US Open champion won his first grass court title at Queen's last month.
"I'm really, really happy to play here again and this time with a win on this really beautiful court," he said. "I wanted to enjoy every single second and I think I did."
Alcaraz said he was learning quickly on grass -- he is playing in only his fourth tournament on the surface.
"I'm playing really, really well on grass. I'm not an experienced guy like other players but I'm enjoying playing on grass... getting better every match that I play.
"Playing here in Wimbledon is something special. You feel different compared to other tournaments."
