The 27-year-old rider completed the 124.1-mile Murrieta to Greater Palm Springs road race in 5 hours, 7 minutes and 40 seconds as temperatures approached 110 degrees.
Acevedo, who rides for American team Jamis-Hagens Berman, leads American Tejay van Garderen (BMC) by 12 seconds with six stages remaining.
Van Garderen, who with Acevedo began the day 16 seconds behind overnight leader Liuewe Westra, finished 12 seconds behind.
Acevedo and van Garderen moved to the front in the final stretch of the 3.7-mile climb to the tram station finish that included an average 8.5 percent gradient.
''I waited for the moment when I felt the strongest,'' said Acevedo, who claimed his seventh career pro win and second in 12 days. ''For me, it was about the same as yesterday although the altitude was higher. I was lucky I stayed away.''
The intense heat and dry desert conditions ravaged the field.
Acevedo, who won the opening stage of the Tour of the Gila in New Mexico on May 1, was among many riders who collapsed at the finish into the arms of support staff.
Marco Pinotti (BMC), who finished the stage and Belgian Pieter Serry (Omega Pharma-Quickstep), who collapsed about a half-mile from the finish, were both transported to a hospital with heat-related issues.
''It was probably the hottest race that I've ever done,'' said van Garderen, the race favorite who placed fourth and fifth overall the past two years. ''Insane. It was unlike anything I've ever done.''
Westra (Vacansoleil-DCM), the stage 1 winner, lost nearly 10 minutes in the stage and is now 37th overall.
Andy Schleck (RadioShack Leopard-Trek), the former Tour de France winner, finished 36th and is now 30th overall, more than nine minutes behind.
''I was afraid to go into the red (zone),'' said van Garderen. ''Sometimes when you go into the red in this heat, you can't recover.''
Phil Deignan (United Healthcare) of Ireland was 27 seconds behind to take third in the stage and is also third overall, trailing by 27 seconds.27 seconds behind and is also third, trailing by 27 seconds.
Americans Scott Zwisanski (Optum/Kelly Benefit), Jason McCartney (Bissell), Ben Jacques-Maynes (Jamis) and Sylvain Chavanel (Omega Pharma-QuickStep) of France escaped from field early and built nearly a 12-minute advantage.
The foursome pedaled at the front for five hours, before the group steadily reduced its deficit approaching the final climb.
The 16-team event, which began with 127 riders, now has 118 remaining. The eight days of riding continues Tuesday with the 110.3-mile third stage from Palmdale to Santa Clarita and concludes Sunday in Santa Rosa after a 727-mile trek.