McCarthy has now allowed just one run in nine innings this spring.
The Angels got on the board in the sixth when Kole Calhoun drew a one-out walk.
D-backs reliever Eury De la Rosa tried to pick Calhoun off first and threw the ball past first baseman Paul Goldschmidt, which allowed Calhoun to advance to third.
J.B. Shuck followed with a sacrifice fly to right to score Calhoun.
Angels starter Garrett Richards was sharp in his spring debut as he allowed two hits and fanned a pair while tossing three scoreless innings.
Richards said he's "just trying not to be a max-effort guy. Just trying to control counts, keep the ball down in the zone, keep a clean, simple delivery, get ahead of guys. But for the most part, just really staying in control of myself and just driving the ball downhill."
The game was one of the ones in Major League Baseball today testing out the new instant-replay system and it did not take long for it to come into play.
Angels manager Mike Scioscia challenged a call in the second inning when Luis Jimenez was ruled out stealing second. After a two-minute, 31-second review, the umpiring crew upheld the decision.
Monday also marked the first appearance of the spring for closer Ernesto Frieri, who watched his wife give birth to the couple's second daughter Friday in Phoenix. Frieri followed Richards to the mound and threw a scoreless inning.
Collin Cowgill went 2-for-2 for the Angels, who tacked on runs in the eighth and ninth innings. John Hester's bunt single in the eighth plated Shuck to make it 2-0, while Andrew Romine's RBI single in the ninth made it a three-run cushion.
The D-backs struck for two runs in the ninth on Nick Ahmed's sacrifice fly and pinch-hitter Rudy Flores' RBI double, which hit high off the center-field wall and missed being a home run by inches.
Up next: The D-backs take to the road to play the Padres at 1:05 p.m. MT at Peoria Sports Complex. Randall Delgado will make the start in place of Bronson Arroyo, who was scratched with lower back stiffness. Addison Reed, who is competing for the closer's job with J.J. Putz, is also scheduled to see action.