In the seventh, Mitch Moreland led off with a single and advanced to second on a passed ball. After Elvis Andrus flied out, Brett Nicholas walked and Delino DeShields singled to load the bases. Dickey left the game responsible for all three runners.
With Gavin Floyd on in relief, Moreland attempted to tag up and score on a Rougned Odor's flyout to Kevin Pillar, but prior to Moreland crossing the plate, DeShields was thrown out by Pillar while trying to advance to second.
Moreland's run initially counted, but a review showed DeShields was tagged out on the 8-6 double play before Moreland crossed the plate, keeping it a 1-1 game.
"I thought [Dickey] was really good. He pitched good enough to win," manager John Gibbons said. "He got out of the jam. We caught a break there when we threw the guy out there at second base before the run had crossed, so he was feeling pretty good.
Dickey feels confident the work he's putting in between starts will translate to wins.
"Just trying to get more in attack mode, I think," Dickey said. "Trying to work ahead in counts a little bit more, I firmed up my knuckleball a little bit more consistently. I carried the velocity through the innings well.
"It usually takes me a little bit to get going, and my hope is that this is the start of 27 more quality starts. That's what I'm working towards."
Texas got on the board in the third when catcher Brett Nicholas took Dickey's 2-1 pitch over the wall in center field for a solo home run. Dickey has now allowed 90 home runs since 2013, the most in the Majors.
Dickey said the Nicholas home run was the product of him tinkering with his velocity.
"I think psychologically it makes a bit of difference," he said. "As far as being able to attack the strike zone with a knuckleball that's 77 [mph] or above, I feel like the margin of error is better.
"I still mechanically pulled off of a few. Even the home run to Nicholas there was kind of one that I ran away from a little bit, tried to guide it in there for a strike, and it just didn't catch and he hit it out. Once I start eliminating those, I'll go deeper and deeper into games."
Dickey could also benefit from more offensive support. In his six starts this season, the Blue Jays are averaging fewer than three runs per game (2.83).
The veteran right-hander doesn't believe the current trend, which saw Josh Donaldson, Jose Bautista, Edwin Encarnacion and Troy Tulowitzki combine to go 1-for-14 in the series-opening loss to the Rangers, will continue for much longer.
"Rarely do you have four or five guys in the lineup not going at the same time. That's rare," Dickey said of the Blue Jays' bats, which combined for 10 strikeouts in Monday's loss. "Everybody is going to have to put in the work that they know they need to do in order to turn the page, but we can fall back on the professionalism in this room.
"I think a lot of guys have taken it personally, and we all should. We'll see where it goes from here, but I'm optimistic."
Dhiren Mahiban is a contributor to MLB.com and covered the Blue Jays on Monday.