Corey Patterson bunted home the go-ahead run in the ninth inning when he dragged the ball on a safety squeeze for Toronto in a 5-2 victory over the AL West-leading Rangers on Thursday.
"He bunted it into no man's land," the 40-year-old Oliver said.
When Oliver (1-2) fielded the ball, nobody was covering the bag with first baseman Davis charging in and thinking about trying to throw home if he got the ball.
Patterson got credited with a single and John McDonald, who held at third base until the ball was safely in play, scored the go-ahead run.
Then the Blue Jays, who took three of four games in the series, added two more runs when Texas made two errors on the same play.
"We'll just wash it down the drain and move on," manager Ron Washington said.
After a 5-5 homestand, and still holding a one-game division lead over the Los Angeles Angels, the Rangers head to the West Coast for seven games in seven days against AL West opponents. They play four games in Oakland and three in Seattle before returning home to play the New York Yankees.
The defending AL champion Rangers have lost nine of 15 games since a 9-1 start.
"We need to play better obviously," Rangers second baseman Ian Kinsler said. "Right now, we don't like the way we're playing. ... Offensively, we need to get better and take it on the road and try and improve."
McDonald and pinch-hitter Yunel Escobar had consecutive one-out singles before Patterson's bunt. After Jose Bautista drew his majors-best 26th walk and Adam Lind struck out, third baseman Adrian Beltre made his first error of the season and Oliver had a throwing error allowing another run.
"Put it behind us," Oliver said. "That's all we can do."
Frank Francisco (1-0), who played his first six major league seasons in Texas before being traded in January, got the final four outs. The right-hander struck out Mitch Moreland after taking over with two on and two outs in the eighth before a perfect ninth.
"I don't really look who's in there. I just face who I got to face," he said. "I feel great."
Rangers starter Alexi Ogando struck out seven with three walks while allowing two runs and four hits over six innings. The right-hander had strikeouts for six of the first eight outs he got.
Brandon Morrow, making only his second start of the season for Toronto, struck out six in six innings with one walk.
"Good pitching battle, both Alexi and Morrow," Washington said. "We had some opportunities, and we didn't cash any of them in, and it just came back and got us."
Bautista walked after Ogando struck out the first two batters in the game. Lind then hit a 411-foot shot into the second deck of seats in right field that ricocheted back onto the field for his third homer of the series. He has 10 homers in his last 14 games at Rangers Ballpark.
Pedro Strop struck out Lind on a 10-pitch at-bat to end the seventh with the bases loaded.
Texas got a run in the first when Elvis Andrus had a one-out walk, stole second and scored on a single by Beltre.
Andrus had another stolen base in the eighth, after his single and 10 pickoff attempts and a pitchout. But he and Nelson Cruz were stranded when Moreland, who hit a game-winning homer Wednesday night, struck out.
Kinsler had a single and stolen base before scoring on Michael Young's sacrifice fly in the third to tie the game at 2. Kinsler added a leadoff double in the fifth before being picked off by catcher Jose Molina on a close play a few pitches later when he dived back into second base.
Shortstop McDonald made a sweeping tag and Kinsler briefly argued to no avail with umpire Paul Emmel after being called out that he gotten his hand on the back side of second base in time. Replays showed that Kinsler may have been right.
NOTES: The Rangers won't have a chance to match their team record for 18 wins in April set in 1998. They have 15 with two games left in the month. They can still match the 17 of 1989. ... Texas has lost 10 of its last 13 games against the Blue Jays. ... Andrus has hit safely in 10 of 11 games, and is 6-for-6 on stolen bases this season. ... Young's 16 RBIs match his career high for April.