Alcaraz, bidding to add a fourth Grand Slam trophy to his cabinet after his maiden French Open triumph last month, dropped serve midway through a high-quality opening set before battling back to clinch it in a tiebreak.
Lajal broke Alcaraz again early in the next set but the dreadlocked world number 269 was unable to make the advantage count and his opponent broke back to love immediately before pouncing again in the 11th game.
With the momentum having swung, Alcaraz continued to reel off the points for a two-set lead and raised his game further in the third to break with a superb backhand crosscourt winner and he never looked back from there to close out the victory.
"He played a good match, which obviously surprised me a little bit because I didn't have the chance to see him play a lot. He has a great level, he's really young, my age," Alcaraz said.
"I'm sure I will play against him even more on the tour and I'm really happy to get my first win on Centre Court this year."
Alcaraz said he still felt a touch jittery at the venue where he beat Novak Djokovic in the final 12 months ago.
"Stepping on this court, it's the most beautiful court I've played on. I still get nerves when I'm playing here," he added.
"I played for 45 minutes here on Thursday and it's the first time I get nervous practising. I'm glad and I'm a privileged guy to play on this court.
"This is a new year, a different tournament, I have to be focused on my game. When I walk around, I get goosebumps. I remember last year and that was a great feeling."