Dave Schmidt yielded seven hits for the first shutout of his major league career and Steve Buechele hit a two-run homer as Texas beat California in Arlington, Tex.
Schmidt (7-6) got out of a bases-loaded jam in the first inning, then settled down to retire the last 13 batters.
"I just don't get used to this club not scoring runs," Angels Manager Gene Mauch said.
"I don't know," he said when asked about the run drought. "If I knew, I'd go in there and fix it. We get the hits. I just don't understand why we don't get the runs."
The Angels left eight runners on base and wasted three hits by Reggie Jackson, who singled in the first inning and doubled in the third and fifth.
Buechele's homer in the sixth inning, after George Wright singled, gave the last-place Rangers a 5-0 lead. Texas scored in the first when Wayne Tolleson singled, advanced to second on an error by Angels' shortstop Dick Schofield and came home on Pete O'Brien's single.
Texas made it 3-0 in the third on O'Brien's RBI double and a run-scoring single by Larry Parrish. Bobby Jones' sacrifice fly in the eighth after Gary Ward triple brought home the final Rangers' run.
Losing pitcher Kirk McCaskill (12-12) gave up eight hits in six innings.