PITTSBURGH -- Toronto Blue Jays manager John Gibbons said he sat awake in his hotel bed Saturday night, thinking about his bullpen's recent problems. He even addressed his group of relievers Sunday morning.
Dustin McGowan made those worries a nonfactor, at least for a day.
"We had to have that one," Gibbons said.
McGowan (2-1) allowed one run, striking out five and throwing 101 pitches.
It was the second consecutive quality start for McGowan, a diabetic who started wearing an insulin pump on the mound in his last start.
"My blood sugar still gets erratic sometimes," he said. "But that's part of the game for me. With the adrenaline going and everything, it does what it wants to do. I can't control it sometimes."
McGowan eclipsed the 100-pitch mark for the first time since June 27, 2008.
"That's two outings wearing that pump," Gibbons said. "Maybe there's something to that."
It was just the fourth win in 13 games for Toronto, which prevented the Pirates from completing their first series sweep of the season.
Pirates manager Clint Hurdle and first base coach Rick Sofield were ejected by plate umpire Greg Gibson at the end of the fourth inning for arguing a called third strike on Jordy Mercer. The strikeout stranded two runners and ended the inning.
"I think it was pretty apparent that the low strike wasn't going to come into play," Hurdle said. "But the fact of the matter was it got to a point where I felt a pitch that hadn't been called a strike all day got called a strike in, for me, a very pivotal at-bat for us."
Rasmus connected in the second inning for his fourth career slam. He also doubled and singled.
The Blue Jays held on to this early lead. Toronto wasted a 5-3, ninth-inning edge in the series opener and a 5-0, fourth-inning advantage on Saturday night.
Josh Harrison hit two triples for the Pirates.
Edinson Volquez (1-3) gave up six runs and seven hits in five innings. He also allowed six earned runs in his last outing April 21 against St. Louis.
Volquez pitched himself into a jam in the second inning before Rasmus stepped to the plate, issuing walks to Edwin Encarnacion and Juan Francisco to start the inning. Brett Lawrie reached on an infield single to load the bases with no outs.
Rasmus hit a full-count curveball about 10 rows deep in the right-field seats for his seventh home run of the season, giving the Blue Jays a 4-1 lead. Rasmus said he was not necessarily looking for an offspeed pitch in that situation.
"I was just trying to be out over the plate and throw my hands at anything because he's got a good changeup, good curveball and a good two-seamer, and he already tried to thumb me a couple in," he said. "I was just trying to be ready to put something in play."
The slam negated an early lead the Pirates built on Neil Walker's groundout, scoring Harrison after his triple.
Harrison also tripled in the eighth and scored on Andrew McCutchen's sacrifice fly.
Toronto's Jose Bautista walked in the fifth to reach base in his 31st consecutive game, the longest active streak in the majors. But he went hitless, snapping a career-best 13-game hitting streak.
Cabrera had three hits, and extended Toronto's lead to 6-1 with a two-run homer off Volquez in the fifth. Rasmus scored another run in the eighth on an RBI single by pinch-hitter Dioner Navarro.
Highly regarded Blue Jays RHP Marcus Stroman made his big league debut, allowing one earned run and one hit while getting two outs. The Blue Jays selected the 23-year-old Stroman Triple-A Buffalo and optioned OF Anthony Gose. ... The Pirates plan to recall LHP Jeff Locke to start against San Francisco on Monday night. An All-Star last year, Locke struggled in the second half of 2013 and did not make the Pirates' opening day roster. ... J.A. Happ (0-0, 4.15) is scheduled to pitch for the Blue Jays at Philadelphia on Monday night.