-Dortmund two points clear of fourth-placed Hoffenheim
-Promoted Leipzig book Champions League group spot
-Werner, Selke score twice each for Leipzig
-Darmstadt relegated after Bayern loss
Borussia Dortmund edged past Hoffenheim 2-1 on Saturday to move into third place in the Bundesliga with two matches left and take a big step towards securing a spot in next season's Champions League group stage.
An early goal from Marco Reus and a late one from Pierre-Emerick Aubameyang sent Dortmund, who are also through to the German Cup final, up to 60 points, two ahead of fourth-placed Hoffenheim, who cut the deficit with a late penalty.
Timo Werner and subsitute Davie Selke scored twice as promoted RB Leipzig crushed Hertha Berlin 4-1 to secure a Champions League group stage spot and a top three finish in their sparkling first season in the Bundesliga.
Lepizig top scorer Werner took his league goal tally to 19 as second-placed Leipzig move up to 66 points.
Champions Bayern Munich, who secured the title last week, beat bottom side Darmstadt 98 1-0 to confirm their long-expected relegation.
With third place guaranteeing more than 12 million euros and fourth leading to the tricky Champions League qualifying rounds, Dortmund looked more determined from the start.
"We delivered from the start an outstanding defensive performance," said coach Thomas Tuchel. "That was the key."
"But that was no final. The season is not over and third place not yet safe. It is very important to maintain our intensity."
Reus put them ahead in the fourth minute from what was clearly an offside position, drilling the ball through the legs of charging keeper Oliver Baumann.
Aubameyang could have doubled the lead 10 minutes later when Dortmund were awarded a penalty for a hand ball in what was another controversial decision.
Reus had controlled the ball with his arm before it bounced off the hand of a Hoffenheim player and referee Felix Brych awarded the spot-kick, triggering angry complaints from the visitors.
Gabon international Aubameyang stepped up but fired his low penalty wide to keep the visitors in the game.
Reus went close to scoring a sensational second goal on the hour but Baumann slapped his powerful volley wide with a reflex save.
He could do nothing when Aubameyang nodded in from close range to join Bayern's Robert Lewandowski at the top of the scorers list on 28 goals.
Hoffenheim pulled a goal back with an 86th-minute penalty from Andrej Kramaric.
VfL Wolfsburg beat Eintracht Frankfurt 2-0 to get some respite in their battle to avoid relegation, moving three points clear of the relegation playoff spot and into 14th on 36 points.