The Rangers' offense failed to capitalize in extra innings on a number of occasions, and eventually their luck caught up to them when the Blue Jays came through with their first run in 15 innings to make Wolf -- who pitched brilliantly in relief -- the loser in a game that extended Texas' losing streak to three games, matching a season high.
"We needed one big hit, and we just couldn't get it," Rangers manager Ron Washington said. "But I'm very proud of the job Wolf did. He did an outstanding job. That's the prototype for what a [long reliever] is supposed to do -- and he did it today.
"[The loss] is not any tougher. But when you play that long, you want to win."
Wolf entered the 18th having thrown six scoreless innings of relief before Davis roped a single down the left-field line to score Emilio Bonifacio -- the first run either team scored since the ninth inning. Bonifacio, who hit a one-out single, made it to third on an errant pickoff throw to first by Wolf which sailed down the right-field line and allowed the speedster to advance two bases.
The 30-year-old Wolf, who threw a career-high 6 2/3 innings, pinned the loss on himself for throwing the ball away, which is something he said he can't remember ever doing before.
"I think that was the first time I threw one away, to be honest with you," said Wolf, who threw 59 of his 82 pitches for strikes. "It doesn't happen very often, and it came at a bad time. It should have never happened."
But if the Rangers had capitalized on the plethora of opportunities they had, Wolf wouldn't have had to hang his head for Saturday's outcome.
Texas continually wasted chances after putting two runs on the board in the ninth off Blue Jays closer Casey Janssen to pin him with his first blown save of the season and force extra innings.
In the top half of the 18th, the Rangers looked like they were finally going to put some runs up after putting two on with none out. But things went south in a hurry after David Murphy, who led off the frame with a double, was picked off second base after leaning too far off the bag on Elvis Andrus' failed bunt attempt.
Third-base coach Gary Pettis told Murphy while he was on second that if Andrus bunted through the ball, he had to give himself enough to space to get back to the bag, which he ultimately didn't.
"That's the last words I heard," Murphy said. "It's a play you anticipate. If you see the ball in the strike zone, you anticipate the bunt so you can try to get as good of a jump as possible.
"I guess I over-anticipated it. ... You can't take a chance there."
Toronto's Brad Lincoln, who was the eighth pitcher the Blue Jays used, went toe-to-toe with Wolf, throwing four scoreless innings of one-hit ball before turning the ball over to Aaron Loup for the 18th. Loup recorded his third win of the season.
The other big missed opportunity for Texas came on a gamble after putting together a big rally in the 10th.
Texas loaded the bases with none out against Toronto reliever Dustin McGowan, who made his first big league appearance since September 2011, before the Blue Jays turned the ball over to left-hander Juan Perez. After recording one out, Perez got Leonys Martin to line out to right, and Jose Bautista completed the inning-ending double play by tossing out Lance Berkman, who attempted to tag up from third, at the plate.
It wasn't even close.
"You have to make them make the throw," Washington said, defending the decision to send Berkman home. "We know Bautista has one of the best arms in the game, and he did what he had to do. I was hoping he overthrew it, underthrew it, did something [bad]. But he made a perfect throw."
Texas was 1-for-19 with runners in scoring position and left 17 men on base. The Rangers were held to three runs or fewer for the sixth time in the club's last seven games.
In what became just a footnote of the game, both starting pitchers threw well.
Blue Jays starter Mark Buehrle threw seven strong innings, allowing one run on a solo homer to Jeff Baker in the seventh, which was just one of four hits Texas mustered against him, while walking two and striking out three.
Buehrle outpitched Rangers ace Yu Darvish, who wasn't at his best, but battled out of a number of jams and finished his performance strong. The one jam he couldn't battle out of, however, came in the third.
Colby Rasmus put Toronto on the board by hitting a two-run triple off Darvish, and came around to score on the play to give the Blue Jays a 3-0 lead after Jurickson Profar made a throwing error to third baseman Leury Garcia that traveled into the stands.
Darvish was sharp from that point on and lasted seven frames, allowing three runs (two earned) on five hits while walking three and striking out seven. It was his ninth quality start in 13 outings, and the 10th straight game he has lasted at least six innings.
Texas has dropped seven of its last eight away from home and fell to 1-4 on its current six-game road trip, in which the club has been outscored 35-15. The rough stretch, coupled with Oakland's hot play, has dropped the Rangers into second place in the American League West.
"If you look at the big picture and look at our body of work this season, I feel like this is the first real, real rut that we have been in," Murphy said.
"And I wouldn't even call it a terrible one."