Touted prospect Yasiel Puig, who hit .526 in Cactus League play but will begin the year at Double-A Chattanooga, hit sixth for the Dodgers and went 0-for-3.
The Quakes won when Angelo Songco drilled a walkoff RBI single into right field with one out in the bottom of the seventh.
"We came out here and we wanted to win and we were able to do that," Songco said. "Nothing like a walkoff .To be able to beat them is a great feeling."
Chris Reed, the Dodgers' first round pick in 2011, started and threw three hitless innings for the Quakes. He walked one and struck out three, including Crawford and Hairston.
"After I was finished throwing it kind of set in (that I struck out major leaguers), but in the moment you just are trying to make pitches," Reed said. "The main thing was not worrying about the names, just throwing strikes and not falling behind."
The Quakes strung together four consecutive singles in the first inning, including an RBI knock by 2012 first-round pick Corey Seager, against Dodgers starter Stephen Fife to jump out to an early 2-0 lead and extended it to 3-0 in the third.
The Dodgers will join the rest of their teammates for two more exhibition games against the Angels before beginning the regular season on April 1.