Bora-Hansgrohe's Majka, who has an overall lead of 2 seconds, edged out Lotto NL-Jumbo rider Bennett to win the stage while third place went to Ian Boswell of Sky and fourth to Lachlan Morton of Dimension Data.
Daniel Jaramillo took the King of the Mountain jersey for the race's fastest climber during the 89.8-mile second stage, which included 9,276 feet of elevation gain and a gruelling climb up Mt. Hamilton.
Latvian rider Toms Skujins left the race after he was involved in a nasty crash during a stretch of downhill while zipping along at about 50 miles per hour.
His team, Cannondale-Drapac, later announced that he had a concussion, a broken left collarbone and road rash. A medical evaluation was ongoing, the team said.
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The seven-day race continues on Tuesday with a ride from Pismo Beach to Morro Bay for stage 3, a 119.6-mile ride that includes 6,375 feet of elevation gain.
This is the twelfth edition of the Amgen Tour of California and the first time the race has been staged as part of the World Tour, a designation that organizers hope will draw more top names in the sport from Europe.
This year, Tour of California is being held at the same time as the Giro d'Italia, now in its 100th year and one of cycling's traditional three "Grand Tours" of Europe. Many of the sport's biggest names are competing there rather California.
The Tour of California wraps up in Pasadena on May 20.
(Reporting by Rory Carroll, Editing by Peter Rutherford)
