Boston (83-72) lost 5-3 to Toronto on Saturday, and were eliminated from postseason contention after Minnesota defeated Baltimore 8-5 later in the day.
The Red Sox had reached the postseason in a record three straight seasons, which included sweeping the Cardinals in the 2004 World Series to end an 86-year championship drought.
Boston was eliminated from AL East contention on Wednesday and may now focus on trying to stay ahead of Toronto (81-73) for second place in the division.
The Red Sox have a 1 1/2 -game lead over the Blue Jays, but Toronto has played one less game. The Red Sox have finished first or second each year since a fourth-place finish in 1997.
“You know you don’t have anything else to play for so you might as well play for that,” Blue Jays first baseman Lyle Overbay said. “Those guys have been in the top two for 50 years or so. It would be a step in the right direction for us. It would mean a change of the guard.”
For Boston to extend the lead over its division rival, it needs to beat Gustavo Chacin (8-3, 4.67 ERA) for the first time this season. The left-hander is 3-0 with a 2.81 ERA in three starts against the Red Sox this year. Chacin also has limited Boston hitters to a .186 average.
He failed to record a decision last Sunday, holding Tampa Bay to three runs and seven hits over 6 2-3 innings of a 5-3 home win.
Kyle Snyder (4-4, 6.28) will try to get back in the win column for Boston. The right-hander limited the New York Yankees to two runs and seven hits over five innings on a 6-3 win in the opener of a day-night doubleheader last Sunday.
He held Toronto to two hits over seven innings on a 2-1 win on Sept. 1 at Fenway Park.
Snyder, who was acquired from Kansas City on June 16, was recalled from the minors by Boston a month later. He’s 3-4 with a 5.72 ERA in 14 appearances, including eight starts, with the Red Sox.
Manny Ramirez made his first appearance in 13 games on Saturday, walking as a pinch-hitter in the seventh. Ramirez has missed 22 of the last 31 games with a sore knee.
Manager Terry Francona, ejected in Saturday’s loss for arguing a call at second base, wouldn’t commit to starting Ramirez in the series finale.
“I don’t think we’ll see that tomorrow or the next day, but we’ll see it how it goes,” he said.
Ramirez has 101 RBIs, the ninth straight season he’s reached that mark.