Jose Bautista hit his second homer in exhibition play for the Blue Jays.
Beltran signed a three-year, $45 million contract with the Yankees in the offseason. He batted .296 with 24 homers and 84 RBIs with the St. Louis Cardinals last year.
"You want to see guys swinging the bat well, obviously, but it's really important at the end," Yankees manager Joe Girardi said.
"It doesn't really matter sometimes. You can be swinging the bat horrible at the end of spring training and get off to a hot start and vice versa. But it's always nice to see."
Bautista connected off Vidal Nuno in the first. Nuno struck out three and gave up two hits in two innings.
Toronto starter Esmil Rogers tossed two innings and allowed an earned run. The right-hander gave up three hits and struck out one.
Yankees shortstop Derek Jeter did not play.
Blue Jays: Rogers threw 36 pitches and worked almost-exclusively on his changeup, which he said is progressing well.
"That's what I was working for," Rogers said. "Down in the Dominican (Republic) during winter ball, I worked on my changeup and now I feel more comfortable. I got it before. The only reason is I didn't have too much confidence to throw that. Right now, I can throw anything I want."
Rogers was 5-9 with a 4.77 ERA in 44 games with the Blue Jays last season. He is a candidate for the fifth spot in the rotation.
Yankees: Nuno said he felt as if he "got a little happy with the fastball," which led to Bautista's home run.
Nuno, who is a contender for the fifth spot in the rotation, appeared in five games with the Yankees last season and made three starts. He finished 1-2 with a 2.25 ERA.
"Overall, I'm just pleased a little bit with how the outcome came," he said. "It was just one pitch and Bautista just hit it out. Location was good and everything. (My fastball) just got overused a little bit and I wasn't using my secondary (pitches) like I was supposed to do."
Blue Jays: Colby Rasmus was scratched from Sunday's lineup because of a stiff neck.
Rasmus was set to bat seventh, but opted to sit as a precaution. He does not expect it to be a long-term issue and hopes to return in a "couple days."
"I feel all right, I just woke up on the wrong side of the bed this morning," Rasmus said.
Anthony Gose took Rasmus' place in center field and was 0 for 3 with a strikeout.
Manager John Gibbons said closer Casey Janssen had an MRI on his sore right shoulder, but it did not show any damage.
"It's just inflamed," Gibbons said. "There's a lot of wear and tear on a guy over the years. He's smart, backed off and we'll give him a little breather. There's still a full month (of spring training) left. He'll be ready to go."
Janssen, who saved 34 games for the Blue Jays last season, said he plans to rest and start throwing again in a few days.
Yankees: Girardi said first baseman Mark Teixeira, limited to 15 games last season because of a right wrist injury, might play in his first spring training game on Thursday or Friday.
Alfonso Soriano, recovering from flu-like symptoms, went through a workout Sunday morning that included batting practice and defensive drills.
The outfielder/designated hitter could play in his first exhibition game in the next few days.
The Yankees dealt with a minor scare before the game when a towel inside of a dryer caught fire in the grounds crew clubhouse located next door to the team's clubhouse.
Girardi joked that "it got a little smoky" and said some players evacuated.
There was no reported damage or injuries.
Yankees fifth starter candidate Michael Pineda, who missed the past two seasons after right shoulder surgery, threw 21 of 35 pitches for strikes in a simulated game.
He faced 10 batters, allowing two hits, striking out one and walking his final two hitters.
Pineda and Hiroki Kuroda are scheduled to pitch in Friday's game against the Tigers in Tampa.