Alex Rios hit a two-run home run to support a strong pitching effort from starter Scott Richmond and help the Blue Jays win for the fourth time in five contests and improve to 12-5.
The streaking Blue Jays have began the season with five straight series victories, the first team to accomplish the feat since the San Francisco Giants in 2003.
"We're finding ways to do it," Toronto first baseman Lyle Overbay told reporters.
"I mean, we didn't really hit the ball well tonight. We got some key hits, those are key hits that we're getting right now."
Richmond struck out eight batters and allowed two runs over six innings to pick up his second win of the year.
Scott Downs threw a perfect ninth inning to get the save and complete a solid night for Toronto's relievers, which included scoreless stints by Brandon League, Jesse Carlson and Shawn Camp.
The Blue Jays used second-inning home runs by Vernon Wells and Overbay to take an early 2-0 lead.
Texas (6-9) outfielder Josh Hamilton was 2-for-4 with a solo home run in the fourth inning while Chris Davis added solo shot to right field in the sixth.
However, the Rangers were 4-1 down by the end of the fifth after Rios delivered his blow off starter Kevin Millwood, who surrendered four runs in seven innings.
Millwood (1-2) lost his second straight and has allowed 10 runs in the last three starts.
Texas second baseman Aaron Hill stayed hot with two hits and two runs as he raised his average to .377.
He has hit safely in 16 of his team's 17 games this year but could not prevent the Rangers from losing for the fourth time in the last six contests.
The Blue Jays have matched their franchise's best start through 17 games.
First-year right-hander Richmond has been especially pivotal for Toronto as the team has starters Jesse Litsch (elbow) and Ricky Romero (abdomen) on the disabled list.
"We've had a couple bad breaks here to start the season," Richmond said.
"But they're not on long DL stints and they're coming back quick. I'm just trying to focus on every time I go out there."
