The Angels had runners against Morton, in his first season with the Astros, in each of his five innings, with the Angels leaving the bases loaded in the second. But Morton (1-1) made the pitches when he needed to.
"He didn't have it tonight, but somehow found a way to put up zeros," Astros manager A.J. Hinch said.
"He just pitched out of that jam," Hinch said. "He would make pitches, especially with the bases loaded. All in all, he was rescuing innings every single inning. He did a great job."
In facing 24 batters, Morton allowed five hits with three strikeouts and two walks.
"It would have been nice if I was in the zone more and executing my pitches better," said Morton, who lowered his ERA to 2.81. "I was able to get some ground balls in different situations.
"My misses were in weird spots, spots they hadn't been. In a good way. The ball was down more, my misses were down. So I think it's a good sign."
The Angels, who had five hits, but none after the fifth inning, stranded two runners in each of the first, third and fifth frames. In the fourth, Morton got Escobar to hit into a 4-3 double play to end the inning.
"It wasn't like I wasn't trying to challenge guys, I was," Morton said. "I threw the ball and a bunch of them came out different."
Morton's cutter was effective and he had some success with his fastball.
"His velocity helped bail him a couple of times," Hinch said.