Lyles (3-1) limited the Angels to two runs on six hits, exiting with a 3-2 lead after walking one and striking out five.
Reliever Brad Peacock surrendered a two-run homer to Hank Conger in the eighth inning, allowing the Angels to pull within a run at 5-4, but Hector Ambriz hurled a 1-2-3 ninth for his second save.
Matt Dominguez provided a two-run single in the top of the ninth while Carlos Corporan and Carlos Pena each launched a solo homer for Houston.
The Angels' C.J. Wilson (4-4) was tagged with the loss, yielding three runs on six hits over 7 1/3 frames.
Mark Trumbo went deep for Los Angeles, losers of five in seven contests overall.