Rodriguez, who is still dealing with pain in his left foot from stepping on a cactus, had allowed only one earned run in his previous three Cactus League appearances. Only one of the four Angels runs against him was earned because of Rodriguez's own error on an errant pickoff throw.
The Brewers were charged with four errors Saturday after committing five against the Rangers the day before.
Trout and Hamilton each had two hits, and Hamilton scored two runs. The Angels have won four games in a row.
"Josh is putting a lot of work in," Angels manager Mike Scioscia said about Hamilton. "He's working hard in the mornings, he's down getting live BP in the lower fields, and he carried that over into the game today and had some good at-bats."
For Milwaukee, Carlos Gomez hit a leadoff home run on the same day manager Ron Roenicke confirmed he'd be the Brewers' leadoff hitter to begin the season. Bench candidate Elian Herrera had two hits and three RBIs, and scored a run in the fifth inning when Lohse blooped a single to right field. On the mound, Lohse allowed four runs, three earned, on eight hits in six innings. He struck out seven.
"The pitch to Trout, I would have been more mad had I walked him than given up the homer," Lohse said. "After that, I kind of settled in. The Hamilton one, he just pulled his hands in -- that ball was off the plate, in. You make your pitch and you have to live with what happens. He did an amazing job hitting that one."
Angels right-hander Joe Blanton started with L.A.'s regular lineup for the first time after pitching in the road half of split-squad games in each of his three starts. Without a spot in the starting rotation he is potential trade bait, but surrendered four earned runs on six hits and four walks in 4 1/3 innings, with three strikeouts.
Up next: Garrett Richards will make his fourth Cactus League start when the Angels host the Indians and right-hander Zach McAllister at Tempe Diablo Stadium on Sunday. Richards, who has a 5.40 ERA in 11 2/3 innings this spring, pitched in a Minor League game against the Triple-A Cubs five days earlier, giving up one run in six innings. Sunday's game starts at 1:10 p.m. PT and can be seen on FOX Sports West or MLB.TV.
Adam McCalvy is a reporter for MLB.com. Read his blog, Brew Beat, and follow him on Twitter at @AdamMcCalvy. This story was not subject to the approval of Major League Baseball or its clubs.