Spain's Alcaraz was untroubled by the former world number three from Bulgaria, pushing his perfect 2026 match record to 13-0 in just 66 minutes.
Djokovic, a five-time Indian Wells champion who has struggled in recent years, had to grind for two hours and 12 minutes to subdue 57th ranked Kamil Majchrzak of Poland 4-6, 6-1, 6-2.
Alcaraz said he was wary of Dimitrov, but even in the swirling winds on Stadium Court he was in control, firing from the baseline with power and accuracy.
He barely broke a sweat and cracked plenty of smiles, saving the lone break point he faced in the second set and even getting a high-five from his opponent on a changeover.
"In general just really happy with the things that I've done today," said the 22-year-old Spaniard, whose Australian Open triumph made him the youngest man to complete a career Grand Slam.
He added the Qatar Open title before heading Stateside to chase a third Indian Wells crown.
"I love being here so much, I think that's why I'm just playing relaxed, playing calm, chilling," he said.
Although he shares the record for most Indian Wells ATP titles with Swiss great Roger Federer, Djokovic has found the early going in California anything but relaxing in recent years.
Djokovic had to grind for two hours and 12 minutes on a windy Stadium Court, Poland's Majchrzak grabbing two quick breaks in the opening set before Djokovic began to find his rhythm from the baseline and assert his superiority.
"Kamil is a very solid player," Djokovic said. "He doesn't have tremendous power, but he has every shot in the book and he was not afraid to come in and take the ball early.
"He played a tremendous first set. I kind of reset and started feeling the ball better," Djokovic added after a match marked by extended, entertaining rallies that included a 40-shot exchange in the opening game of the third.
Majchrzak held in that game, but Djokovic broke him twice on the way to a 5-2 lead and was finally looking more relaxed when he closed it out with a backhand volley winner.
It was an especially satisfying win for Djokovic given his recent struggles in the California desert.
He shares the record for Indian Wells titles with Swiss great Roger Federer, but hasn't made it to the quarter-finals since he last won in 2016.
Last year he lost to Dutch lucky loser Botic van de Zandshculp in his second-round opener while a year before he fell to Italian lucky loser Luca Nardi in the third round.
"It's kind of hard to find my A-game, particularly at the beginning of the tournament," he said. "So just glad to overcome a challenge."
Draper rallies
Britain's Jack Draper launched his title defense with a 3-6, 6-3, 6-2 victory over Spain's Roberto Bautista Agut.
Draper halted Alcaraz's bid for a rare Indian Wells three-peat in the semi-finals last year before beating Holger Rune in the final.
That victory launched his rise to fourth in the world, but he returned to California in rebuilding mode again after an arm injury forced him to cut short his 2025 season.
"To come out and play the level I'm playing after the injury I had, I am really proud of that," said Draper, who made his return to the tour in Dubai last week having not played since his second-round withdrawal at the US Open.
"It was difficult," the oft-injured Draper, now ranked 14th, said of his latest comeback bid. "Even though from the moment I got here last week, I have felt the love and special feelings being back here, but at the same time I haven't played in a long time and have had a difficult injury, so mixed emotions.
"But I am really glad with the way I came through in the second and third sets against a formidable opponent in Roberto."