"He certainly did what he needed to do," manager Ron Washington said of Cruz. "It was huge right there, because we really weren't doing much against [Carlos Villanueva]."
The Rangers struggled to get to Villanueva, Toronto's starter, early but came through in the fifth.
Adrian Beltre started off the frame with a ground-rule double to right-center field on a ball that would have been a routine catch had Anthony Gose not lost it in the sun. Texas proceeded to take advantage.
Cruz drilled the very next pitch over the wall in left for a two-run homer, his 19th of the year, to give the Rangers a 2-1 lead.
That was all the Rangers mustered off Villanueva, who lasted 6 1/3 innings, allowing two runs on four hits while walking one and striking out four. It was Villanueva's third consecutive quality start and sixth in nine outings since joining Toronto's rotation in late June.
"Always impressed with him," Washington said. "I don't know how he gets away with that stuff, but he does. He's a change-speeds master."
Cruz's home run dug the Rangers out of an early deficit.
Oswalt retired seven straight batters to start the game before issuing a four-pitch walk to Gose in the third inning.
After Gose stole second for his 10th swipe of the season, Oswalt balked, which moved him over to third with one out and Adeiny Hechavarria at the plate.
Hechavarria brought Gose home with an RBI single to left to put the Blue Jays ahead, 1-0.
Oddly enough, Oswalt balked again the next inning after hitting slugger Edwin Encarnacion with a pitch to start off the frame, which moved him to second base with nobody out. But Oswalt regrouped and stranded two runners to get out of the inning untouched.
Oswalt allowed a single up the middle to Gose to start the fifth and was removed for Robbie Ross after recording two outs. Washington said prior to the game that he was targeting 75 pitches for Oswalt, but he took him out after 62, choosing to get a left-on-left matchup with Ross facing Colby Rasmus. Ross got Rasmus to pop up to third to end the inning.
"That's his decision," Oswalt said. "He's the manager, I just pitch."
Oswalt, who surrendered one run on two hits over 4 2/3 innings while walking one and striking out five in a no-decision, was originally signed by Texas to start, but he was sent to the bullpen following the Rangers' non-waiver Trade Deadline acquisition of Dempster, who did not travel with the team to Toronto.
The 34-year-old Oswalt will head back to the bullpen once Dempster rejoins the team Monday, and made it no secret what he prefers to do.
"I've started 330 games in the big leagues, I don't think I need to prove myself," he said.
Oswalt felt his stuff was better than he anticipated it being, considering he hadn't started since a July 30 defeat against the Angels. He felt his pitches were crisp from the start and that he was able to carry it through until he departed.
Washington said the two had a talk after he took Oswalt out of the game, but he said it was strictly about the team.
"First two innings, he was as sharp as a tack," Washington said. "You could see in the third and fourth innings he was starting to labor a little bit ... but being the veteran that he is, he locked in and did what he had to do."
Ross went back out for the sixth and allowed three singles to load the bases with two outs for Gose, but he managed to retire him with a 93-mph fastball on the 10th pitch of the at-bat to escape the threat.
The Rangers were forced to get out of another bases-loaded jam in the seventh, as Tanner Scheppers, who relieved Ross, allowed a pair of hits before walking Encarnacion to put three on for David Cooper. Texas turned to Michael Kirkman, who retired Cooper and got Yunel Escobar to pop up to end Toronto's rally.
"[We're in the] seventh inning with the bases loaded and just the one out, but we couldn't cash in," Blue Jays manager John Farrell said.
Mike Adams worked the eighth before turning it over to Joe Nathan, who set a club record by converting his 22nd consecutive save with a perfect ninth. It's also the longest active streak in baseball.
"Between Ross and Scheppers and Kirkland, we got the ball to the point where we wanted it, and that was to Mike Adams and Joe Nathan, and they were outstanding," Washington said.
Kirkman was credited with the win, his first of the season. He said he doesn't care what his role on the team is and is simply enjoying the ride.
"Joe and Mike have been outstanding this year," said Kirkman. "It has been really fun to watch."
Texas improved to 5-3 against Toronto, guaranteeing the club its first season series victory over the Blue Jays since 2006.