"Offensively we did a lot of good things," Scioscia said. "We scored a couple of runs with outs but I think for the most part we pressured them a lot. We just couldn't get either the hit or contact we needed at the right time to at least get a run across."
The Angels have a combined 11 runs in their last five games, and four of them came in Tuesday night's win.
Goldschmidt's 19th home run came in the first inning.
"He is a very smart hitter, very patient and he hits your mistakes," Santiago said. "It was weird because I threw three pitches in and then the fourth one he just seemed like, 'This is what I was waiting for.' It was like it was exactly like he was waiting for that pitch."
Castillo hit his fourth homer — second since coming to the Diamondbacks — leading off the fourth.
Goldschmidt had two hits to raise his batting average to .363, best in the majors. He has reached base in 27 consecutive games, the longest active streak in the majors. He also made a couple of diving stops at first base.
Chase Anderson (3-1) allowed two runs and seven hits in six innings for his second straight win.
"I felt good overall. My stuff wasn't there like it was my last couple of starts," he said. "That's part of the process. We have a really good defense and we made some really good plays to help me out tonight. And the home runs definitely helped."
The four-game interleague series shifted to Arizona after the teams split two in Anaheim.
Anderson, who allowed one hit in seven scoreless innings at San Francisco in his previous start, blanked Los Angeles through four. The Angels were hitless until Kole Calhoun lined a single over the head of second baseman Chris Owings with one out in the fourth.
Los Angeles made it a one-run game in the sixth, but it could have been worse for Arizona.
Calhoun's single and Mike Trout's double put runners at second and third with no outs. Diamondbacks shortstop Nick Ahmed made a diving stop of Pujols' sharp grounder, got to his feet and just got Pujols at first as Calhoun scored on the play.
"He went a far way to get that ball," Goldschmidt said. "He's one of the best shortstops in the league. He's unbelievable. It might have saved the game there."
Trout advanced to third on a flyout but was stranded when Johnny Giavotella lined to third.
Both teams squandered big scoring opportunities, Arizona in the sixth and the Angels in the seventh.
Arizona had runners at first and third with no outs in the sixth when reliever Cam Bedrosian struck out Ahmed, then Owings was caught in a rundown between third and home. Owings mistakenly thought the squeeze was on.
"Just a missed sign at a bad spot," Diamondbacks manager Chip Hale said.
Pinch-hitter Cliff Pennington grounded to first to end the inning.
"It looks good if I get that ball down," Aybar said. "I tried to bunt it to first, second base. Most of the time that is what I do. It was a good pitch. That is baseball."
Calhoun flied out to short center, then Daniel Hudson came on and got Trout to bounce out to third.
Diamondbacks: RHP Archie Bradley (right shoulder tendinitis) is slated to pitch a simulated game on Thursday.
Angels: Los Angeles wraps up the four-game, home-and-home series with LHP C.J. Wilson (4-5, 3.60 ERA) on the mound in an afternoon game.