The Yankees will play further into October after Sunday.

There was a time this summer, as the season teetered on the edge of bitter disappointment, that those words might have elicited great excitement for Yankees fans. But after an embarrassing loss to the Tampa Bay Rays on Saturday put the team back in a precarious position, the idea of playing one more game isn’t necessarily a good thing, not yet.

As recently as Friday afternoon the Yankees seemed poised to host a wild-card game on Tuesday. Now, they face the possibility of getting tangled up in a madcap four-way tie for the two A.L. wild cards that would need to get unraveled on Monday.

In a familiar script for a team that has chased all of its successes with failures, the Yankees put together an impressive 5-1 road trip, vaulting into first place in the wild-card standings, but could not close things out cleanly despite returning home for its final series of the season needing only two wins to secure a playoff spot for a fifth straight year, and home field advantage in the wild-card game.

Facing Tampa Bay proved to be an especially dispiriting way to go down. The Rays, the best team in the American League, won a narrow victory on Friday in the Bronx, and then demolished the Yankees, 12-2, on Saturday.

Brandon Lowe hit three homers for the Rays and knocked in seven runs as Tampa Bay hit the 100-win plateau for the first time in franchise history. The Rays further established themselves as the elite team in the league, while the rest of the A.L. East bumbled around for the two wild-card spots, taking turns going hot and cold.

“Just a bad day for us and we’ve got to get over it quickly,” lamented Aaron Boone, the Yankees manager.

Boone has uttered that sentence in some form several times this season, and on some notable occasions the team responded well. But Saturday’s loss, combined with victories by Boston, Toronto and Seattle, leaves the suddenly stumbling Yankees in danger of needing to play an extra game just to win a wild-card berth that only a few days ago seemed already in their grasp.

“The way this season has gone, it kind of makes sense it would come down to the very last day,” Brett Gardner, the Yankees outfielder said. “It seems about right.”

The final-day scramble starts around 3 p.m. for all 30 teams, but the top intrigue is focused on the teams fighting for the American League wild cards. (The Dodgers and Giants could finish in a tie for the National League West title, but the loser of a potential tiebreaker game would still make the playoffs as a wild card.)

In the A.L., the Yankees and Red Sox are tied with 91 wins apiece while Toronto and Seattle sit on 90.

If the Yankees beat the Rays Sunday, they are guaranteed one of the two wild-card positions, and if that were combined with a loss for the Red Sox in Washington, the wild-card game would be at Yankee Stadium on Tuesday night. But if both teams win, Boston would host the game by dint of their 10-9 regular-season advantage over the Yankees.

In the high-stakes games, the Yankees are sending Jameson Taillon to pitch against Michael Wacha, while the Red Sox have their left-handed ace, Chris Sale, going against Joan Adon of the Nationals, who is making his major league debut. Advantage to Boston.

But Toronto and Seattle are still alive, and the wildest possibility is a four-way tie. For that to happen, the Yankees and Red Sox need to lose, while the Blue Jays and Mariners would both need to win. All four teams would then have 91 wins. What follows in that case would be two tiebreaker games on Monday, with the four teams choosing or receiving one of four designations to determine who plays whom, and where.

The most likely outcome in that scenario would be the Yankees traveling to either Boston or Toronto to play a tiebreaker game on Monday.

It is also possible to have three-way ties for either the first or second wild cards. Those rules are actually more complicated, requiring two days to complete, and would necessitate pushing the A.L. wild-card game back.

The simplest solution for the Yankees is to take care of their own win and then see where the rest of the teams land.

“We obviously can control our own destiny, in a way,” Gardner said.

But the Yankees could have avoided all of this uncertainty by winning Friday or Saturday. Instead, Jordan Montgomery allowed seven runs in two and two-thirds innings on Saturday, keeping the Yankees joined with Boston and Toronto in a conga line of mediocrity that has seen several weeks where none of the teams seemed interested in seizing the opportunity.

Boston, reeling after they were swept by the Yankees at Fenway Park, then lost two out of three to the Orioles, the worst team in baseball. It seemed as if they had jettisoned all hope before they recovered to win twice in Washington to tie the Yankees.

The trendy Blue Jays, with their potent young offense, lost two of three at home against the Yankees, and five of their last eight games going into their final series with the Orioles in Toronto.

Only Seattle, the hottest team in baseball since the middle of August, has played with any consistent determination the last month. But even they lost at home to the Angels on Friday night before beating Los Angeles, 6-4, on Saturday to set up a captivating final day.

The Rays, who have already locked in the best record in the American League, are not playing for much, but even so, can’t help but show their seeming superiority.

“That’s really good team over there,” Gardner said of the Rays, “but a team that if we’re going to make the playoffs — and ultimately get to where we want to go — a team that we’re going to have to beat and go through.”

Thanks to the Yankees’ poor timing, Sunday will be quite a day for baseball. Monday could be even better.