Adrian Beltre added a solo homer as the Rangers snapped their season-high, eight-game losing streak and won for just the second time in 13 road games.
"It was a solid game all the way around," Rangers manager Ron Washington said. "We made all the plays. That's the way we have to continue to play."
Promoted from Triple-A Round Rock on Thursday, Arencibia was booed by the crowd of 38,012 before each of his at-bats, but silenced his detractors with a first-pitch homer off R.A. Dickey (7-10) in the seventh, his second.
"It's kind of flattering when they boo you. It gives you a little bit more fire," Arencibia said.
Arencibia caught Dickey's knuckleball during spring training and at the World Baseball Classic last year, but didn't handle the former Cy Young winner again after a trio of passed balls on opening night in 2013.
"I got to catch it and I really didn't catch it," Arencibia said. "It's a little bit easier to try and take swings at it."
Washington said Arencibia gives the Rangers "some threat" in the lineup, and was pleased to see him succeed on his return.
"I hope it gives him confidence," Washington said. "He certainly didn't lack it when he arrived here from the minor leagues."
Darvish (9-5) won for the first time in three starts, allowing one run and five hits in 6 2/3 innings. He reached the 10-strikeout plateau for the sixth time this season, all in his past 12 starts.
"Darvish was outstanding," Blue Jays manager John Gibbons said. "He can carve you up pretty good."
The Blue Jays went 0 for 10 with runners in scoring position and left nine stranded.
"They had some traffic on the bases and (Darvish) was able to make some pitches in those situations and shut the inning down," Washington said.
Beltre opened the scoring with a leadoff drive in the fifth. Two outs later, Arencibia was hit by a pitch and scored on Rougned Odor's triple. Odor finished 3 for 4, coming within a homer of the cycle.
Colby Rasmus connected off Darvish to begin the bottom of the seventh, Toronto's first homer in five games. One out later, Josh Thole walked and went to third on Munenori Kawasaki's ground-rule double. Darvish left after getting Jose Reyes to fly out, and Neal Cotts came on to retire Melky Cabrera.
Dickey lost for the sixth time in seven starts, allowing five runs and six hits in seven innings. The right-hander, who walked none and struck out seven, has received only five runs of support over his past four starts.
"We're not winning his games," Gibbons said. "We're not scoring runs in his games. But take away that home run, I thought he was really good."
Toronto has scored two runs or fewer in seven of the past 11 games, going 2-9 in that stretch.
Arencibia made his first career appearance at first base. He's the eighth different player to start at first for the Rangers this season.
Texas catcher Geovany Soto made his season debut, batting ninth. Soto, who was activated off the 60-day disabled list Thursday, underwent surgery after tearing ligaments in his right knee during spring training.
Toronto struck out a season-high 17 times. ... Washington said Shin-Soo Choo will not play the outfield on Toronto's artificial turf. Choo, who started at DH Friday, has been bothered by a sore left ankle since late April. ... Minor league coordinator Jayce Tingler is coaching first base for the Rangers on this road trip because Bengie Molina is away for personal reasons. ... Toronto optioned RH Chad Jenkins to Triple-A Buffalo to clear a roster spot for LH Brad Mills, who was acquired on waivers from Oakland Thursday. ... Blue Jays RH Marcus Stroman (4-2) will face Rangers RH Colby Lewis on Saturday. Lewis allowed a club-record 13 runs, 11 earned, against the Angels in his final start before the All-Star break.