They were a swing away from beating the Rangers again before falling short despite a 14-hit outburst.
Mitch Moreland led off the seventh inning for Texas with a tiebreaking home run against Octavio Dotel, and the Rangers held on for a 7-6 victory.
Juan Rivera's solo homer with two outs in the top of the seventh off rookie Cody Eppley tied it at 6.
The Jays had two runs or less in five of their previous eight games before winning the first two in Texas behind an offensive barrage.
"We swung the bats exceptionally well again," manager John Farrell said. "We fought back, responded to the six-run (third) inning. Yet we came up on the wrong side. But there were a lot of good things offensively."
Moreland sent an 0-1 pitch from Dotel (1-1) over the center-field fence for his third homer.
Adam Lind, who homered twice in Toronto's 10-3 victory on Tuesday night, went 2 for 4 with an RBI. He didn't hit one out — he had gone deep nine times in his last 12 road games against Texas.
With closer Neftali Feliz sidelined with right shoulder inflammation, the Rangers have been forced to take a mix-and-match approach at the end of tight games.
The Jays almost gave 40-year-old lefthander Darren Oliver a blown save. Oliver needed 22 pitches for his second save of the season.
Oliver registered the first two outs of the ninth, then yielded back-to-back singles to Lind and Rivera.
Edwin Encarnacion gave Oliver a battle, lasting nine pitches before he struck out swinging.
Toronto starter Jo-Jo Reyes was on the mound for all six runs in the third, although none were earned because of a one-out throwing error by third baseman Encarnacion.
Reyes allowed six runs and five hits in 2 2-3 innings. He hasn't won since June 13, 2008, having gone 23 starts since his last victory.
"I couldn't make the one pitch and they capitalized on our mistakes. It all snowballed," Reyes said of the third inning.
In the top of the third, Lind's sacrifice fly and Rivera's RBI single gave Toronto a 2-0 advantage.
Reyes was on the verge of escaping the third, but Encarnacion's low throw on a one-out grounder by Yorvit Torrealba eluded first baseman Lind and opened the door for the six unearned runs.
"(Encarnacion) makes a backhand play on the line....if that throw is a foot shorter, it's a long hop and it's an easier pick (for Lind)," Farrell said. "But it was a tough ball to dig out of the dirt."
In the fourth, the Jays had a two-out rally on Mike McCoy's RBI single and Jose Bautista's two-run double to cut the deficit to 6-5.
NOTES: Encarnacion had missed the previous four games with a sore left wrist. ... The Jays have still won nine of their last 12 games against the Rangers. ... Bautista has reached base in 20 of his 21 games this season.