The Yankees came into the series opener 15-11 against the division this season, and had won four of their last six against AL East teams, including a three-game sweep of the Blue Jays at Yankee Stadium last week.
"Playing a team that's ahead of us in our division, you have a chance to make up ground," said Girardi. "And they think they've got a chance to put in some separation. It's important to both teams."
Girardi said he expects that, in the end, the winner of the division will be the team that best handles injuries.
The Yankees have endured their share of injury troubles this season, but have weathered those challenges relatively well.
The team's rotation has been hit particularity hard in that regard, with starters Ivan Nova, Michael Pineda and CC Sabathia all on the disabled list.
"I've often said that I believe this division might be won by the team that handles the injuries the best," said Girardi. "[The Blue Jays] have had some [injuries] pop up.
"We've had to deal with some things this year, too. And I think our guys have done a pretty good job. Asking guys to fill in holes that maybe they weren't expecting to. Giving us a chance to win almost every night. You lose 60 percent of your rotation, it's not easy to replace, and we're right there in the middle of it. So we're in a pretty good situation, in a sense."
After wrapping their three-game series in Toronto on Wednesday, the Yankees will host the Red Sox and Rays in back-to-back three-game series.
Jamie Ross is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.