Peralta's homer to right gave Arizona a 3-0 cushion.
The homer came off Royals starter Kris Medlen, who allowed six hits over his three innings.
De La Rosa had his finest outing of the spring, scattering four hits while striking out five and not allowing a walk in four innings.
The Royals looked to have an early rally going in the first when Paulo Orlando and Mike Moustakas collected back-to-back singles to open the game, but De La Rosa fanned Lorenzo Cain and got Eric Hosmer to ground into an inning-ending double play.