The Rays also acquired Jesse Crain from the White Sox in a non-waiver Trade Deadline deal in July, but he remains on the disabled list with a right shoulder strain.
"[Our bullpen] is strong, but if you can make it stronger, you want to do that," Maddon said. "You never walk away from Jesse Crain. Wesley was available and we think he looked good last night. I liked the appearance. He's done some really good work. It gives us another option from [the left] side. There are different ideas we have with him."
Wright, making his Rays debut on Tuesday, inherited a baserunner from starter Chris Archer in the top of the sixth inning and gave up an RBI triple to Dustin Ackley before retiring the next three batters he faced, two of them via strikeouts.
"I want them to know what they're going to get every time and know that I can get outs in big situations," Wright said. "I'm trying to fit into a great bullpen. Guys have welcomed me and I'm real excited to be here."
Sam Strong is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.