Spain thrashed Macedonia 31-20.
The results left Olympic champions Denmark top of main round's Group II with six points from four games, ahead of Spain who have four points from three matches.
The Germans, who have had a patchy tournament, are third on four points from as many games and will need to beat Spain in their final group match on Wednesday as well as other results to go their way to stand any chance of advancing.
World champions France and Croatia top Group I with six points each, although the French have a game in hand. The top two teams from each group will reach the semi-finals.
The clash of handball titans in the Varazdin Arena served up a physical first half, with Germany recovering from a two-goal deficit to lead 9-8 at the interval after failing to score in the opening 10 minutes.
The floodgates opened after the break and Denmark gained a decisive 26-23 advantage in the closing stages as they landed more blows in a thrilling rollercoaster after the lead had changed hands several times.
Germany forced a tense finish after scoring two quick goals but ran out of time as they gained possession of the ball only three seconds before the buzzer.
Denmark's 36-year-old winger Hans Lindberg rolled back the years to rifle in nine goals from 11 shots and pack leader Mikkel Hansen added five.
In the evening fixture, former world champions Spain never looked back after taking a 7-1 lead and boosted their hopes of lifting their first European title after Eduardo Gurbindo netted a game-high six goals.
(Writing by Zoran Milosavljevic in Belgrade,; Editng by Pritha Sarkar)
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