"That was my goal, to have a three-up-three-down inning. It's always your goal when you go out there," said Thornton.
The Red Sox hope the lefty specialist can become a reliable fixture out of the bullpen after acquiring him from the White Sox a couple of days before the All-Star break.
"I just need to get the ball out of the middle of the plate," Thornton said. "I made some mistakes over the plate and got beat on those. Just made better pitches. I feel more and more comfortable every day here. It's a great clubhouse and a great team, and I just want to do my part."
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. Michael Periatt is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.