The right-hander often pitched effectively with the Red Sox, as 12 of his 16 appearances were scoreless. He allowed more than one run just one time.
Boston manager John Farrell was impressed what Wilson's work earlier this season and said he could pitch in Thursday's series opener with the Orioles, if needed.
"He's had two days down, so he's available," Farrell said. "He did a good job [last time] and threw strikes, and seemed to attack lefties and righties both, and he's starting to get his feet on the ground for a young guy. He's got the capability to go multiple innings. We're comfortable with him being here."
Aceves came up Wednesday and made a spot start in Tampa Bay, getting the win in Boston's 2-1 victory over the Rays.
He allowed just one run on four hits in six innings, struck out three and walked four. Aceves improved to 3-1 with the win.
Jeff Seidel is a contributor to MLB.com. Teddy Cahill is a reporter for MLB.com. Follow him on Twitter at @tedcahill.