It turned out to be a winning plan.
There was no sign from third base coach Brian Snitker for Heyward to steal third.
"It was all on my own," Heyward said. "I knew I had a great chance at taking a base and putting some pressure on them and they ended up throwing it away."
Heyward opened the 10th with an infield single off Francisco Cordero (1-4) and moved to second on pinch hitter Jack Wilson's sacrifice. With rookie Andrelton Simmons at the plate, Heyward took off for third base. Arencibia's throw skipped past third baseman Brett Lawrie and into left field, allowing Heyward to score the winning run.
When Heyward saw the ball headed toward left field, he said his reaction was, "I'm home free."
"It was huge," he said. "It paid off. ... I knew it was over. We were rewarded. You take a gamble right there, and that's why you did it."
Heyward already has 10 stolen bases, one more than his 2011 total. He had two hits, including a run-scoring double in the Braves' two-run sixth.
He said he is running more "to put pressure on the defense."
"If I get the base, even if they don't throw it away, it's still a man on third with one out," Heyward said.
Cristhian Martinez (3-1) pitched a scoreless inning for the Braves, who remained one game behind first-place Washington in the NL East.
Heyward scored on Chad Beck's balk in the sixth to give the Braves a 3-2 lead.
"It wasn't a balk," Blue Jays manager John Farrell said tersely.
Heyward was on third as Simmons tried to steal second. Beck turned to throw to second, but no one was covering the bag. Beck then looked to third.
Jose Bautista homered for Toronto.
Both teams stranded a runner at third in the ninth.
Rajai Davis led off the inning with an infield single off Craig Kimbrel and stole second as pinch hitter David Cooper struck out. Davis also stole third before Kimbrel struck out Lawrie and ended the inning on a fly to left by Colby Rasmus.
Toronto pitchers issued seven walks, including four to Uggla. Kyle Drabek gave up three runs and six hits and walked four in five innings.
Atlanta starter Brandon Beachy also was wild. He gave up two runs and three hits and issued a season-high five walks in five-plus innings.
Drabek began the night third in the American League with 41 walks and added two in the third inning to help the Braves take a 1-0 lead. Beachy, who had two hits, singled and moved to third on Michael Bourn's double. Drabek loaded the bases by walking Brian McCann with two outs before also walking Uggla to force in Beachy.
"We walked in a run and the winning run scores on an error," Farrell said.
Beachy couldn't retire a batter in the sixth. Bautista's 16th homer, into the seats in left field, tied the score at 1. Beachy gave up a single to Encarnacion and a walk to Kelly Johnson, his final batter. Encarnacion scored later in the inning on Arencibia's grounder.
Freddie Freeman, who had been out since bruising his left index finger Wednesday, struck out as a pinch hitter in the sixth and remained in the game at first base.
The Braves retired John Smoltz's No. 29 in a pregame ceremony. Smoltz also threw out the first pitch, which he later confirmed was a four-seam fastball to McCann.
During his speech, Smoltz mentioned Farrell, who was Boston's pitching coach in 2009 when Smoltz pitched for the Red Sox during his final season.
Blue Jays 1B coach Torey Lovullo was away from the team for personal reasons. Coaching assistant Luis Rivera filled in. ... Attendance was 42,488. ... Braves 3B Chipper Jones (bruised left calf) had one hit and two walks as he began an injury rehabilitation assignment with Class-A Rome. Atlanta manager Fredi Gonzalez said Jones' assignment could last three days. ... Encarnacion, who had been out since he was hit by a pitch on his right wrist Sunday, started at first base. ... Davis started in LF after missing one game with a jammed left middle finger. ... Toronto rookie RHP Drew Hutchison (5-2) will face RHP Tommy Hanson (6-4) on Saturday.