Marco Richter scored his first Bundesliga goal as Augsburg beat Eintracht Frankfurt 3-0 on Sunday, while a late Filip Kostic goal rescued a point for Hamburg in a 1-1 draw with Hanover.
The win sees Augsburg move up to seventh, while Frankfurt miss an opportunity to go second in the Bundesliga and remain sixth, one point adrift of fourth-placed Borussia Dortmund in the race for Champions League qualification.
After Kevin Danso had missed a sitter early in the game, Augsburg took the lead on 19 minutes, Koo Ja-cheol holding the ball up well in the penalty area before squeezing it into the far corner.
Frankfurt responded brightly, Luka Jovic hitting the post just minutes later, but it was Augsburg who had the better of the first half, as good chances came and went for Caiuby and Gregoritsch.
Marcel Heller forced a smart save from Lukas Hradecky just after the break, as Augsburg continued to dominate.
With 15 minutes to go, the home side finally doubled the lead, Gregoritsch hooking the ball out of the air and prodding it in from close range.
With just minutes to go, the 20-year-old Richter broke into the box and fired the ball into the bottom corner to pick up a first goal in just his second senior appearance for Augsburg.
The draw kept struggling Hamburg just three points from safety and they have now not won in eight Bundesliga games.
Felix Klaus forced an athletic save from Hamburg goalkeeper Christian Mathenia before Hanover broke the deadlock in the 37th minute.
Picking up a poorly cleared corner, Iver Fossum whipped in a fine volley from outside the area.
Mathenia saved Hamburg again on 50 minutes, denying Ihlas Bebou from close range, but the home side remained blunt in attack.
With four minutes to play, though, Kostic latched onto a cross from Sejad Salihovic, bundling in a scrappy equaliser at the far post.
Hamburg then survived a late scare when Kyriakos Papadopoulos gave away a free-kick on the edge of the penalty area, picking up a second yellow card in the process.