Diaz, who went 2-1 with 11 saves and a 2.20 ERA in 27 regular-season appearances for the Travelers, hit 97 mph with his fastball at Progressive Field.
"His stuff comes out hot," Angels manager Mike Scioscia said with a sly smile. "I was glad we could get him out there today at the end."
Diaz was the losing pitcher on Saturday when Arkansas was eliminated from the Texas League North Division playoffs against Tulsa. He allowed three runs in one inning, blowing a save opportunity.
Scioscia said the big league club needed an additional reliever because left-hander Wade LeBlanc was unavailable after pitching three straight days.
"We've been forced to piece some games together from the fifth or sixth inning on, which is why we have so many guys in the bullpen right now," Scioscia said. "You can never have too many pitchers at this point of the season."
To make room for Diaz on the 40-man roster, infielder Ryan Wheeler was designated for assignment. Wheeler was claimed off waivers from the Rockies on Aug. 2, and he was immediately optioned to Triple-A Salt Lake.
Brian Dulik is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.