TORONTO -- Nathan Eovaldi threw a bullpen session on Tuesday as he works his way back from a procedure in late April to remove loose bodies from his right elbow.

Eovaldi threw 35 pitches, including his cutter and splitter for the first time, which left manager Alex Cora encouraged. Now, one of the club's challenges will be easing Eovaldi along at the right pace as the right-hander is very eager to get back on the mound.

"This is a guy that, as everybody knows, we've got to make sure that we slow him down," said Cora. "If it was up to him, the progress would be very fast. His stuff was really good. He was in a good mood in the training room after that."

Cora said on Monday that he expects Eovaldi to need another bullpen session, a decision they'll make when they see how his body reacts to Tuesday's action, but his return will be a welcome sign for the Red Sox's rotation. Over Eovaldi's first four starts of the season in April, he posted a 6.00 ERA and struggled with control, but his velocity numbers were still on par with 2018.

Martinez sidelined by illness

J.D. Martinez was out of the Red Sox's lineup again on Tuesday night as he's dealing with an illness, making it back-to-back games that the slugger has missed after his scheduled day off on Monday.

Martinez was sick throughout the night leading into Tuesday morning, so Cora made the decision early in the day to leave Martinez out of the lineup.

"Hopefully it's only a 24-hour thing and he'll be back tomorrow," Cora said prior to the game. "He'll probably hit during the game and see how he feels. If necessary, we'll use him."

Martinez is well on his way to another strong season at the plate, hitting .308 with nine home runs and a .910 OPS through his first 44 games.

Pedroia, Holt continue rehab with Triple-A Pawtucket

Dustin Pedroia and Brock Holt each made another rehab appearance with Triple-A Pawtucket in their 11-8 win on Tuesday night. Each played seven innings defensively, but the high-scoring game allowed them to get five plate appearances.

Holt started at shortstop and went 1-for-5 with a double and an RBI while Pedroia went 1-for-5 with a single. Prior to Tuesday's game, Cora noted that these reps would be particularly valuable to Pedroia.

"I think the defensive part is not an issue, it's just a matter of the build-up and, obviously, the at-bats," Cora said. "That's something that he wants to keep working at, keep building and keep getting better."