Hammel allowed two runs on three hits over five innings of a 65-pitch outing. He went through the first three innings unscathed before surrendering a run in the fourth.
"I got my work in, so let's leave it at that," said Hammel, who struck out three and walked one. "I was up in the zone. I was happy with my [two-seam fastball]. I was out there getting my work in and throwing strikes."
Hammel, who tossed 43 strikes, is scheduled to toss the third game of the opening series against the Twins on Sunday at Oriole Park at Camden Yards.
Wada, who had Ronny Paulino serve as his catcher, allowed one run on five hits over five innings that included an extra two batters in the last frame. Wada tossed 75 pitches, 50 strikes.
J.J. Hardy hit a solo home run off Wada in the fourth inning.
Up next: The Orioles' final exhibition game will be in Norfolk, Va., where Baltimore faces its Triple-A affiliate at 3 p.m. ET on Wednesday. The team will use a squad of relievers in the game, including Brian Matusz, who is scheduled to pitch five innings.
Chris Girandola is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.