Hamburg SV, in danger of losing their record as the only ever-present team in the Bundesliga's 55-year-history, lost 3-0 at Eintracht Frankfurt on Saturday but were given a stay of execution after rivals VfL Wolfsburg were also beaten.
Hamburg, who had two goals disallowed and hit the woodwork on a cruel afternoon at the Waldstadion, stayed two points behind Wolfsburg, who were thumped 4-1 at RB Leipzig and stayed in the relegation playoff spot.
The odds are still heavily stacked against Hamburg as they would have to beat Borussia Moenchengladbach at home next Saturday and hope that Wolfsburg, whose goal difference is better by 10, lose at home to bottom club Cologne.
After all that, they would face a two-leg playoff against the third-placed team in the second division.
Champions Bayern Munich came from behind to win 3-1 at relegated Cologne but only after Niklas Suele had given the bottom club the lead with his third own goal of the season, and Schalke qualified for the Champions League with a 2-1 win at Augsburg.
Third-placed Borussia Dortmund, however, missed a chance to make sure of their Champions League place when they suffered a shock 2-1 home defeat by lowly Mainz 05 who ensured their survival in impressive style.
Hamburg thought they had gone ahead in the 27th minute when Tatsuya Ito broke clear and buried the ball past Lukas Hradecky but, after Hamburg had celebrated the goal, it was disallowed for offside by the video assistant referee (VAR).
Replays showed that the Japanese player was centimetres offside, if at all.
To add insult to injury, Marius Wolf put Eintracht ahead four minutes later with a shot between Julian Pollersbeck's legs.
Hamburg, one off the bottom in 17th place, were also denied an equaliser when a long-range Douglas Santos effort was tipped on to the post by Hradecky and Lewis Holtby's headed goal from the rebound was disallowed for offside.
Omar Mascarell sealed Hamburg's fate with a deflected goal and Alexander Meier added a third in injury time.
Ademola Lookman became the first English player to score two goals in a Bundesliga game since Tony Woodcock in 1987 when his brace helped Leipzig to beat Wolfsburg.
Timo Werner and Jean-Kevin Augustin scored the other Leipzig goals and Daniel Didavi replied for Wolfsburg who are in 16th place with 30 points.
Bayern's Suele became the first player to score three own goals in a season since Manfred Kaltz in 1977/78 when he flicked a cross into the net after half an hour at Cologne.
James Rodriguez and Robert Lewandowski scored twice in three minutes in the second half to put Bayern ahead, both goals set up by Thomas Mueller, and Corentin Tolisso turned in a Rodriguez cross for the third.
Two goals by Thilo Kehrer gave Schalke a 2-1 win at Augsburg as they made sure of second place with 60 points.
Dortmund remained third on 55 after their defeat, three ahead of Hoffenheim, who were beaten by two Mario Gomez goals in a 2-0 defeat at VfB Stuttgart, and Bayer Leverkusen, who drew 0-0 at Werder Bremen.
Leipzig, sixth with 50 points, also have an outside chance of a top-four finish and a Champions League place next season.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)