Japan striker Yuya Osako scored twice as Bremen stole the lifeline of the relegation/promotion play-off place from Fortuna Duesseldorf, who lost 3-0 at Union Berlin and were relegated with Paderborn, finishing one point behind Bremen.
"We put in a great performance under pressure," said Bremen coach Florian Kohfeldt after the club's 1,900th Bundesliga game.
"But we are aware that we haven't achieved anything -- in the relegation play-off, the emotions will be even greater."
Bremen have spent more seasons than any other team in the Bundesliga, having only spent one term in the second tier, in 1980-81.
Bremen will face second-tier opponents in either Heidenheim or possibly neighbours, rivals and fellow struggling giants Hamburg in the play-off first leg on Thursday.
"I have experienced a few derbies, but I don't care who we face. I just want to appeal to the fans to stay home to watch it," added Kohfeldt, with games still behind closed doors due to the coronavirus pandemic.
A burst of goals from Osako, Milot Rashica and Niclas Fuellkrug -- all in the space of eight minutes -- had Werder 3-0 up at the break against Cologne at the Weserstadion.
Former Everton midfielder Davy Klaassen then fired home a rebound just after the break before Osako, facing his old side, added his second and USA international Josh Sargent completed the rout. Dominick Drexler pulled a goal back for Cologne.
Four-time Bundesliga champions Werder also needed a favour from Berlin and got one as Union beat Fortuna 3-0 with goals from Nigerian duo Anthony Ujah and Suleiman Abdullahi either side of veteran midfielder Christian Gentner's effort.
Bremen will find out their opponents on Sunday, with Heidenheim currently in the play-off place ahead of the final round of matches in the second division.
- Hundred up for Bayern -
At Wolfsburg, Bayern striker Robert Lewandowski scored a penalty for his 34th league goal of the season, finishing as the top scorer for the fifth time.
Kingsley Coman, Michael Cuisance and Thomas Mueller also got on the scoresheet as Bayern, champions for the eighth straight season, finished 13 points clear of second-placed Borussia Dortmund following a 4-0 win.
Mueller set up Coman for Bayern's opening goal to finish the campaign with a league record 21 assists, and his goal that rounded out the win was also Bayern's 100th league goal this season -- one short of the Bundesliga record.
"I am proud of the way we have played over the past few months," said Bayern coach Hansi Flick, who has won 28 of his first 31 games in charge.
Flick also hailed the efforts made to ensure the Bundesliga became the first top European league to resume following the coronavirus lockdown.
"The Bundesliga has led the way in Europe, which was an outstanding achievement," added Flick. "In this respect, this is a very special championship for us."
- Gladbach into Champions League -
Meanwhile, Borussia Moenchengladbach and RB Leipzig secured qualification for next season's Champions League after 2-1 wins over Hertha Berlin and Augsburg respectively, as fifth-placed Bayer Leverkusen missed out by two points despite beating Mainz 1-0.
Dortmund, who had already wrapped up second place, crashed to a 4-0 home defeat by Hoffenheim, for whom Croatia striker Andrej Kramaric scored all four goals, including a no-look penalty.
That result allowed Hoffenheim to leapfrog Wolfsburg and take sixth place, although both sides will go into the Europa League next season along with Leverkusen.
Before kick-off in Dortmund, Mario Goetze, who scored Germany's winning goal in the 2014 World Cup final, was given a send-off by the club with his contract expiring this month.
Elsewhere, Timo Werner signed off with a brace in RB Leipzig's 2-1 win at Augsburg in what was his final appearance for the club before moving to Chelsea.
Schalke's disastrous second half of the season was completed with a 4-0 thrashing at the hands of Freiburg as they finished the season 12th, having been third in December.
Eintracht Frankfurt beat bottom side Paderborn 3-2 in Saturday's other game.