"He's going down the line 100 percent and moving good on defense," Melvin told the Tribune. "Next up for him is to get multiple-hit games back-to-back."
Nakajima's rehab assignment can only last until May 23, at which point he'll either have to be placed on the active roster or assigned to the minor leagues. He's recovering from a left hamstring injury.
The hitless game dropped Jaso's line to .250/.339/.313 with just one home run in 128 plate appearances this season.
Working his way back from forearm tightness, Burnett is expected to be activated from the disabled list before Tuesday's game.
Santana has managed to last at least six innings in each of his eight starts this year while compiling a 2.77 ERA. He'll face his former team, the Angels, Thursday.
The win broke up a string of losses in five straight game for Milone, moving him to 4-5 on the year. He takes that record, a 3.47 ERA and a 49:12 K:BB ratio into a matchup with the Astros Friday.