Park was scratched just before his scheduled start because the Rangers planned to trade him to the San Diego Padres for slugger Phil Nevin, a deal that awaited approval from the commissioner's office.
Wasdin started and allowed just one run and four hits in 4 2/3 innings. He was told after batting practice that the trade could happen.
"I was told 'Be ready just in case' and then about 6:30 I got the final word," Wasdin said. "Hopefully, I showed what kind of role I can do."
Texas manager Buck Showalter said Nevin will arrive in Toronto on Saturday.
"Phil sounds real excited," Showalter said.
First baseman Mark Teixeira was thrilled to get him.
"He's been a great hitter his whole career. He's a big right-handed bat that we could definitely use," Teixeira said.
Park, who left the Rogers Centre before the game ended, is 8-5 with a 5.66 ERA in 20 starts this season. Since signing his $65 million, five-year deal three years ago to become the Rangers' No. 1 starter, the 32-year-old right-hander is 22-23 in 68 starts. He has been on the disabled list five times, plagued primarily by back problems.
"His first couple of years were tough because he was injured the whole time, but this year he was a positive force for us. He did everything we asked him to do. He kept us in games," Texas shortstop Michael Young said.
"This year was a different year for Chan Ho. We really enjoyed having him around. It was a positive year for him, and I'm confident he's going to do really well for the Padres," he said.
Young said he wouldn't be surprised if they Rangers made another deal.
Friday was Korean day at the Rogers Centre, and some fans brought signs in support of Park.
Doug Brocail (4-2) got the win, pitching 2 1/3 perfect innings. He struck out four.
Gary Matthews Jr. led off the game with a home run, the sixth time Texas has done that this year.
Corey Koskie drove in Toronto's lone run with an RBI double in the fourth. Texas ended Toronto's three-game winning streak. The Blue Jays beat the Los Angeles Angels in an 18-inning game the night before, the longest game in team history.
"I'm pretty tired. It was a long day yesterday. The longest game many of us have ever played in," Toronto center fielder Vernon Wells said. "I think it took a toll on us, unfortunately."
Downs, who replaced Pete Walker in the rotation, allowed two runs and five hits in five innings, striking out a career-high eight and walking two in his second start of the season. The 29-year-old left-hander gave up five runs and four hits in 2 2/3 innings of a 12-10 loss to the Rangers on July 9 in his other start.
Toronto ace Roy Halladay expects to be activated from the disabled list next week, less than a month after a bone in his left leg was broken. Halladay threw 57 pitches in a simulated game Friday and might return for Tuesday's game against the White Sox. The 2003 AL Cy Young Award winner was struck in the left shin by a line drive off the bat of Mench on July 8. ... The Blue Jays played 18 innings on Thursday, but Showalter had no sympathy for them. "We got to our hotel room at 4 a.m. two days in a row. I don't want to hear about 18 innings when they are at home and get to sleep in their own bed," Showalter said.