His bat was a big boost a few hours after a players-only meeting for a slumping team trying to halt a slide down the AL West standings.
"I'd like to see him do that more often, then he can get more playing time," manager Ron Washington said after Moreland doubled in his final at-bat. "Mitch is a big part and today he stepped up huge for us."
Washington expects Fielder to play in the next game Tuesday night against Seattle after he had an injection designed to ease the pain and pressure of a disk problem in his neck that he says goes back to last season.
If the outlook on Fielder changes, Moreland says his approach won't.
"We've had to deal with adversity all year," said Moreland, whose second homer of the season was a line drive just over the wall in right field off R.A. Dickey (4-4) to break a 2-all tie. "You come in every day ready to play."
The Rangers, who snapped a four-game losing streak and stayed seven games behind Oakland in fourth place in the AL West, had gone 23 innings without an extra-base hit when Rios drove one off the right-center wall in the fourth.
"Great teams find a way to sweep series," Dickey said. "We're definitely going in the right direction, but there's more there that we need to do. Today was a game we probably should have won."
The Rangers were in position to add to the lead Moreland gave them in the seventh when Toronto manager John Gibbons got the Blue Jays out of the jam with a challenge after three previous visits with umpires ended without a video review.
Michael Choice lined out to Francisco, who tagged third base with his glove as Robinson Chirinos was diving back to the bag. Dale Scott called Chirinos safe, but a review lasting nearly 3 minutes overturned it and gave Toronto an inning-ending double play.
Moreland hit his second homer of the season after Rios just beat Francisco's throw for an error on one of the plays Gibbons considered challenging. Toronto had a season-high four errors.
Texas rookie right-hander Nick Martinez left with a 2-1 lead after five innings but lost the chance for his first big league win on Encarnacion's ninth homer, a shot to left field off Aaron Poreda in the sixth.
Poreda (2-0) ended up getting the win after a scoreless seventh, and closer Joakim Soria pitched a shaky but scoreless ninth in a non-save situation on his 30th birthday.
Francisco's home run into the upper deck in right field was among four hits allowed by Martinez in a solid outing that should give him a chance to stay in the rotation with four Texas starters on the disabled list. He had never pitched above Double-A before this year.
"Each time he takes the ball it's an experience for him," Washington said. "He knew where we were today and he did a good job just getting us through as many pitches as he could handle."
Dickey allowed three hits and four runs in falling to 12-12 against the team that drafted him and gave him his first shot in the majors 13 years ago.
Rangers 2B Rougned Odor was a late scratch with a sore right wrist. He was replaced in the No. 9 spot by Luis Sardinas. ... Sunday marked the first of nine day games in a stretch of 14 for the Rangers. That hasn't happened since 1984. ... Julio Franco, who spent five of his 23 seasons in Texas and was 49 when he played his final game in 2007, threw out the ceremonial first pitch.