Neshek's perfect two-batter outing meant he's retired 33 of the 35 right-handed hitters faced this season, holding them to an AL-low .057 average.
"It was good to see Neshek and Sipp step up in the eighth," Hinch said. "We have a deep bullpen, and tonight showed it."
Keuchel's length -- on the heels of Mike Fiers not getting out of the fourth Friday -- and the three relievers used Saturday enabled Hinch to stay away from Ken Giles and Will Harris, who had been worked hard in the last series.
"It's the first time, after a start, in a while where the team won, and I can smile," said Keuchel, a 20-game winner in 2015. "I knew it was going to turn around, because I'm a pretty good competitor."
It was his eighth victory against the division-rival Angels, his most against any opponent. It started somewhat ominously, when Keuchel gave up back-to-back, two-out home runs to Angels sluggers Mike Trout and Albert Pujols. The Astros ace had never allowed more than one homer in a game to the Angels before.
"Two bad pitches to two good hitters," Keuchel said.
After Johnny Giavotella opened the bottom of the second inning with a single, however, no other Angel reached base.
"My breaking ball got a lot better," Keuchel said. "I was able to command it."
Catcher Jason Castro added: "He's shown some glimpses [lately] of how he's been pretty much all of the past two years. It was just an adjustment, to get back to what you do right."
Keuchel noted two things that have hampered him, despite being fine physically.
"At times, I've tried to slow the game down too much, and that's not my game," he said. "It started with me pressing a little bit too much, trying to be too perfect."
It all came back Saturday, however, resulting in what Castro called "old Dallas."
Earl Bloom is a contributor to MLB.com who covered the Astros on Saturday.