The Spanish 21-year-old dropped serve twice in a two-hour, 23-minute encounter before prevailing 7-6 (7-3) 7-5 6-2.
The world No.3 now meets Australia's Aleksandar Vukic who will be hoping his fine form on grass will enable him to stun the tennis world.
Alcaraz has been joined in the second round by world No.1 Jannik Sinner, plus fellow seeds Daniil Medvedev (5), Casper Ruud (8), Grigor Dimitrov (10), Ugo Humbert (16) Frances Tiafoe (29) and Zhizhan Zhang (32).
But Sebastian Baez (18) and Nicolas Jarry (19) were knocked out, by Brandon Nakashima - who now meets Australian Jordan Thompson - and Denis Shapovalov respectively.
Russia's Daniil Medvedev returns during his straight sets win over American Aleksandar Kovacevic. (AP PHOTO)
Former three-time grand slam champ, the oldest man in the tournament at 39, Stan Wawrinka also progressed.
Alcaraz, seeking a fourth grand slam 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 tie-break.
Lajal broke Alcaraz again early in the next set but the dreadlocked world No. 269 was then broken back, to love.
Alcaraz then upped his game, easing to victory.
World No.1 Jannik Sinner plays a backhand return during his win over Yannick Hanfmann. (AP PHOTO)
The champ 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.
"When I walk around, I get goosebumps. I remember last year and that was a great feeling."
Australian Open champion Sinner did not have it quite so easy against Germany's Yannick Hanfmann.
Hanfmann, playing his third match at Wimbledon after a pair of first round defeats, delayed the world No.1 long enough to force a pause while the No.1 Court roof was closed as the light was fading.
But under the floodlights Sinner prevailed 6-3 6-4 3-6 6-3.
Medvedev beat American Aleksandar Kovacevic 6-3 6-4 6-2.
The 28-year-old Russian, beaten in the semi-finals last year by Alcaraz, took 106 minutes to dispose of the 88th-ranked New Yorker, who could not cope with his booming serve and whipped forehand.
Ruud was made to work hard by Australian qualifier Alex Bolt 7-6 (7-2) 6-4 6-4, and then relayed how a food bug had derailed both his French Open campaign and his Wimbledon preparation.
The 25-year-old Norwegian's bid struggled to deal with what was then an unknown stomach issue in Paris as he lost to Alexander Zverev.
"I went home the day after (losing at Roland Garros) and kept feeling quite bad for a full week... lying in bed all the time. I had no appetite," Ruud said.
"I took some tests and found out that I had this kind of uncommon small parasite that I had been infected with through not sure where. The most normal place where you can get infected from it is through unclean water.
"It is most likely like vegetable, fruit, or salad being washed with unclean water. It can take up to 12 days before it kicks in and you feel symptoms, so it's very difficult to know where I got it."
Ruud had been to Spain, Italy and Switzerland before Roland Garros and has no idea where and how he ended up getting the ailment.
"I did think if this keeps on going on for too long, Wimbledon might be at risk," he added. "I didn't have any appetite. I had very low energy and slept a lot and was just in bed pretty much the whole time."
with agencies
10°C