It marked the third homer of the spring for Lowrie and fifth for Norris, who upped his Cactus League average to .382.
Beckett went just one more inning for the Dodgers, leaving after four with seven runs and six hits charged to him, along with three walks and a strikeout.
Like Beckett, A's starter A.J. Griffin gave up two home runs, but he also fanned eight against just one walk in 4 2/3 innings, giving up four runs in that time.
Griffin, pegged as the A's No. 4 starter, surrendered a two-run homer to right fielder Andre Eithier in the first, before offering up a solo shot to left fielder Carl Crawford in the third.
Los Angeles catcher Tim Federowicz led off the fifth with a base hit and came around to score on a sacrifice fly off the bat of Matt Kemp.
Dodgers up next: The long-awaited return to exhibition action for pitcher Zack Greinke will be Monday night, when he will start for the Dodgers on the road against Kansas City and Wade Davis. Greinke last pitched in a Cactus League game on March 1, as he missed starts with the flu and a sore elbow that has responded to a platelet-rich plasma injection. The game also might mark the return to the lineup of first baseman Adrian Gonzalez, who was scratched Sunday with a bruised right forearm.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.