Tuesday's poor performance continues a bad stretch for one of the league's most potent lineups. The Rangers are batting .245 (202-for-825) over their past 25 games, dropping their season average from .281 to .266.
Tallet allowed just two hits over seven strong innings of work. He struck out three and induced 12 popups.
"I had a good changeup," Tallet said. "That's the equalizer. There were a lot of popups, a lot of bad popups."
The Rangers have now dropped four straight to the Blue Jays after winning their first head-to-head matchup this season against Roy Halladay in Toronto. After Tuesday's loss to Tallet, who is a lefty, Texas is 13-8 against left-handed starters this season and 4-5 against southpaws at home.
The best opportunity for the Rangers to score came in the second inning, but it came with two outs.
Nelson Cruz led off the inning with a flyout to center, and Marlon Byrd followed with a strikeout. Brandon Boggs then doubled deep to left field before Chris Davis walked to put runners on first and second with two outs. Tallet responded by striking out Jarrod Saltalamacchia.
Elvis Andrus walked to lead off the third, but he was then forced out on an Ian Kinsler double-play ball. From there, Tallet retired 13 of 14 batters. His lone blemish came on a Davis single with one out in the fifth inning.
"He wasn't consistent in the strike zone," Washington said. "From the dugout, I don't know if his stuff was good. But we were too aggressive. We didn't allow him to get into trouble."
The Rangers were set down in order in the first, fourth and sixth by Tallet. The Blue Jays' bullpen then threw two perfect innings, retiring the side on six pitches in each inning.
Emergency starter Doug Mathis allowed five runs -- four earned -- over five innings of work on 98 pitches. He walked three and struck out none.
Mathis gave up four of those runs in the second inning. Vernon Wells laced a triple that Byrd barely missed catching and then scored on a groundout by Adam Lind. Mathis allowed back-to-back walks before Kevin Millar singled home Scott Rolen.
Elvis Andrus then booted a tailor-made double-play ball off the bat of Rod Barajas. That set up a single by Marco Scuturo that scored Miller and Lyle Overbay, who extended his hitting streak to 15 games.
"I didn't help myself too much," Mathis said. "I got to do a better job going to attack hitters. I was falling behind hitters.
"They're a good hitting lineup. I just got to do a better job going after hitters."
Mathis is now 1-2 with an 8.46 ERA in five career starts for the Rangers. He said that learning about drawing Tuesday's start just last night had no impact on his outing.
"That shouldn't be any excuse," Mathis said. "Starting today shouldn't have been any different. I've been a starter all season."
Rangers starters have thrown at least five innings in 40 of their past 44 outings, but yet the rotation features a 5.66 ERA over the past 15 games.
The newly acquired Jason Grilli pitched a perfect ninth inning in his Rangers debut. The Rangers brought in Grilli in a trade with the Rockies earlier in the day.