By SABC Sport
7th July 2023
Alcaraz was given a stern examination by France's Muller during a contest that lasted two hours and 33 minutes, but ultimately progressed 6-4 7-6 (2) 6-3.
It made it seven consecutive wins on grass for the top seed, who is viewed by many as the most likely candidate to stop defending champion Novak Djokovic in his pursuit of a record-equalling eighth title at the All England Club.
Alcaraz quickly dismantled Jeremy Chardy in round one, making it 13 sets in a row for the Spaniard on grass after he won at Queen's last month.
Nerves appeared to be present for the world number one on only his second appearance on Wimbledon's main stage having lost there to Jannik Sinner last year.
Despite a classy forehand winner on the run from the second point of the contest, Alcaraz struggled early on and had to save three break points during his second service game.
First seed Alcaraz sprayed 10 unforced errors in the opening half an hour, but a 135mph ace seemed to ease his tension and he clinched a break in the next game as he edged a tight opener.
Muller, ranked 84 in the world, continued to take the match to Alcaraz, who saw four break points come and go at the start of the second set.
Alcaraz eventually had to go to a tie-break and he reserved his best tennis for the crunch moment. A volley at the net got him off the mark and he followed up with a succession of drops shots that helped him claim the second set.
It had been a hard-fought set for Alcaraz but after nearly two hours on court with the roof open and temperatures hitting 29 degrees, the US Open champion showed his extraordinary athleticism during the opening exchanges of set three.
More break point opportunities were squandered by the 20-year-old, but he eventually did break for only the second time in the match at 4-3 up in the third.
Alcaraz brought up match point with a 116mph ace and, although Muller briefly stole the show with a stunning backhand return, another big forehand winner from Alcaraz confirmed his 42nd win of the season.
During his on-court interview, Alcaraz said: "I am really, really happy. My second match on Centre, my first one I lost last year.
"Really happy to play here again and this time with a win. It is a beautiful court. I wanted to enjoy every single second and I think I did.
"I am playing well, gaining more experience and getting better with every match I play.
"Playing here in Wimbledon, it is something special. It feels different compared to other tournaments so it is very special to play here.
"It is an amazing energy I receive and I hope to keep going like this."