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.
Up Next for the A's: The A's will play host to the Brewers on Monday afternoon, with right-hander Bartolo Colon getting the start against Milwaukee lefty Chris Narveson beginning at 1:05 p.m. PT at Phoenix Municipal Stadium. Newcomer Nate Freiman is scheduled to make his first start at first base for the A's.
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.