The world number two took the interruption to clear the bees from the court in his stride before racing past Zverev 6-3, 6-1 in little more than 90 minutes to keep his title defence on track.
Zverev did not play badly but Alcaraz's all-court game was just too good, the 20-year-old Spaniard sealing the victory by breaking the German for the fourth time and taking his winning streak in the Californian desert to 10 matches.
"It was strange, I've never seen something like that at a tennis match," twice major champion Alcaraz said of the invasion of bees, during which he was stung on the forehead before heading for cover.
"I'm not going to lie, I'm a little bit afraid of the bees. Once the match started again, I managed to stay away from the bees and do the things I needed to do."
Italian Sinner earlier continued his perfect start to the season by cruising past Jiri Lehecka 6-3 6-3 to improve his win-loss record this year to 16-0.
A windy, cool day did little to slow down the hottest player on the men's tour as Sinner was in control throughout, facing a single break chance the entire contest while his opponent piled up unforced errors.
"In the morning, it was really, really windy," Sinner said in his court-side interview. "The first set was tough to handle.
"He has huge potential so I was really aware of every point that I made and in a way I am just happy because I make the semi-finals last year and this year I have again a chance to play in the semis in one of the greatest tournaments we have throughout the whole year."
Lehecka reached his first Masters 1000 quarter-final with upset wins over fifth seed Andrey Rublev and 11th seed Stefanos Tsitsipas but had no answers for the lanky Australian Open champion.
The third seed quickly had his Czech opponent under pressure by collecting the first break in the third game with a massive forehand winner before closing out the set with a second break.
It was much the same business-like approach in the second as Sinner again claimed the early break to get 3-1 ahead and he held serve on the way to a 19th straight win including three from the end of last season.
Local hope Tommy Paul also reached the semi-finals with a 6-2, 1-6, 6-3 win over Casper Ruud and will take on Australian Open runner-up Daniil Medvedev, who powered past Holger Rune 7-5, 6-4 to stay on course for his first title of the year.
Medvedev claimed a high-quality opening set and came from a break down in a tense second, during which he was struck on the body by a Rune backhand on the first point, before wearing down the young Dane for the victory.
