Instead, their early momentum was snuffed out by all-too-familiar base-running gaffes.
The Yankees, meanwhile, took advantage of their chances and powered their way to an 11-4 victory in front of 25,875 spectators at Rogers Centre.
New York (91-66) maintained its one-game lead on Baltimore in the American League East, while Toronto (69-88) remained tied with Boston for last place in the division after the Red Sox dropped a 9-1 decision to the Orioles.
The Blue Jays had several early chances against Yankees starter Hiroki Kuroda but couldn't capitalize. Toronto left seven men on base over the first five innings — including six in scoring position.
Yunel Escobar and Canada's Brett Lawrie both made mistakes on the bases.
Lawrie, from Langley, B.C., doubled in the first inning and started to break for third when Colby Rasmus hit a chopper to the first-base side. Lawrie turned around and dived back to second but couldn't beat Nick Swisher's throw to Jeter, who applied the tag.
Escobar was burned an inning later. He doubled and moved to third on a wild pitch but was picked off by Canadian catcher Russell Martin after a Kelly Johnson strikeout.
"There's a difference between being alert and aware," said Toronto manager John Farrell, whose team has made a number of baserunning mistakes in a disastrous 2012 campaign. "And yet the over-aggressiveness took guys out of their position."
Swisher's two-run double put New York ahead in the first inning. The Blue Jays tried to chip away at the Yankees' lead throughout the game but couldn't get the big hit when they needed one.
Martin hit a career-high 20th homer of the season — a three-run shot — in New York's four-run sixth inning that put the game out of reach.
"That three-run homer really opened up a little bit," said Yankees manager Joe Girardi. "They seemed to have runners on in every inning, so I mean they had opportunities to tie the game up."
Toronto starter Chad Jenkins (0-3) lasted 3 2-3 innings in his second major-league start.
"I didn't throw a lot of strikes, I was kind of all over the place," Jenkins said.
Kuroda (15-11) worked 5 1-3 innings and pitched his way out of several jams thanks in part to New York's defence. He allowed 10 hits but gave up just two earned runs.
"We answered his pitches with some hard-hit balls," Farrell said. "We took ourselves out of a couple of those run-scoring situations with some anticipation that didn't work out well."
Colby Rasmus hit a solo shot for his 23rd home run of the season in the fifth inning to get Toronto on the board.
Adam Lind added a two-run shot — his 11th homer of the year — in the seventh inning and Rajai Davis had four hits to tie a career high.
Eric Chavez added some insurance for the Yankees in the ninth with a two-run blast, his 15th homer of the season.
Notes: Jenkins made a nifty catch in the first inning. He snagged a Curtis Granderson liner but the momentum lifted his glove right off his hand. The glove flew about five feet into the air and Jenkins caught it — with the ball still inside — for the out. Granderson laughed after the unusual play. ... Jenkins made his first start last Sunday, lasting five innings in a 3-0 loss to Tampa Bay. ...The retractable roof at Rogers Centre was closed in the second inning. ... Blue Jays reliever Bobby Korecky made his first appearance with Toronto in the ninth inning. He is the 53rd different player the team has used this season, equalling the club record from 2011 and 1999. ... . New York outhit Toronto 13-12 in a game that took three hours 43 minutes to play. ... Toronto left-hander Ricky Romero (9-14) will get the start on Saturday afternoon for the third game in the four-game series. The Yankees will counter with Andy Pettitte (5-3). ... Toronto closes out the regular season next week with a three-game set against the visiting Minnesota Twins.