A day after Brian McCann's indecision at first base cost the Yankees in their first loss to Toronto in the Bronx after 17 straight wins, two more mistakes cost them a chance for a series win.
Betances' two-base error set up a go-ahead sacrifice fly for Munenori Kawasaki in the eighth inning. After New York tied it in the bottom half, Robertson's lapse let Bautista move into scoring position ahead of Dioner Navarro's RBI single.
After rallying three times Sunday, the Yankees lost 5-4 to the Blue Jays to drop their first series at Yankee Stadium to Toronto in nearly two years.
"Our miscues is what cost us in this series," Yankees manager Joe Girardi said. "We've got to be better at that."
Bautista reached on a fielder's choice against Robertson (1-3), stole second without a throw and scored on Navarro's liner to center field for the final lead.
"I just let him slip. I didn't think he'd be going, Robertson said. "I just didn't have my sharp stuff."
Bautista was running on his own.
"I just took a chance and said I'm going to try and take a hop step when he comes set, and if he doesn't fake, I'm going to run," Bautista said. "He went to the plate, and I had the easiest stolen base. I got in scoring position early in the at-bat for Dioner."
Aaron Sanchez (1-0) gave up Carlos Beltran's tying RBI hit in the eighth. Kawasaki had put Toronto ahead with a flyball that followed Betances' wild throw. The first-time All-Star opened the inning with a walk to Colby Rasmus.
"My cleat got stuck," Betances said. "As soon as that happened I had a feeling I was going to throw it away."
The Blue Jays won for the seventh time in 10 games following the All-Star break — the same record as the Yankees. But their first series win in New York against the AL East rival since Aug. 27-29, 2012, sent Toronto to Boston with a one-game lead over the Yankees for the second AL wild card.
"They beat us," Derek Jeter said. "That's the bottom line."
Juan Francisco homered off Shane Greene leading off the fifth to put Toronto up 2-0. But Chase Headley hit his first homer with the Yankees, a drive off J.A. Happ, and two pitches later Francisco Cervelli hit his first homer in 15 months to tie it in the sixth.
Casey Janssen pitched the ninth for his 16th save.
Jeter made two nice stops at shortstop and Brendan Ryan, a shortstop playing second base, also flashed some impressive leather while playing in front of Colorado Rockies shortstop Troy Tulowitzki, who wears No. 2 to honor his favorite player as a kid. The injured star was on the East Coast for a second opinion on his hip flexor from a doctor in Philadelphia.
Jeter said he wasn't aware Tulowitzki was at the game — or that he was hurt.
Bautista had a run-scoring grounder to first base after Jose Reyes led off the game with a single and Melky Cabrera doubled. Francisco led off the fifth with a drive into the second deck in right field for a 2-0 lead.
But Happ gave it all back in a three-pitch span in the bottom half. First, Headley hit a drive deep to left. With a 1-0 count, Cervelli sent a shot to right-center that glanced off a leaping Cabrera's glove and hit the top of the right-field wall.
Rausmus put Toronto back up with a double to left-center in the sixth, chasing Greene after 5 1-3 innings.
"I got to have a short memory, but that one hurt," Greene said of the pitch to Rasmus.
Greene allowed eight hits and three runs in his second straight difficult outing after beginning his career as a starter with two outstanding outings.
NOTES: The Yankees have given up 43 unearned runs this year. They allowed 38 all last season. ... Yankees 1B Mark Teixeira (back strain) hit off a tee and soft toss, and fielder grounders. Girardi said Teixeira is still day to day. Girardi also said Beltran is still at least a week away from returning to OF. He's continuing with his throwing program. Beltran hasn't played the outfield since May 11 because of a bone spur. "I'm trying," Beltran said. ... Up next: The Blue Jays are at the Boston Red Sox. R.A. Dickey (8-10) will start Monday. The Yankees head to Texas for three games. David Phelps (5-4) pitches for New York.