Holders Bayern Munich and Bayer Leverkusen both reached the German Cup quarter-finals with a 2-0 win at Augsburg and a 2-1 win at Freiburg respectively.
Mario Mandzukic scored in the first-half before being shown a straight red card, and captain Darijo Srna scored two minutes after the break to give Croatia a 2-0 victory of visiting Iceland to book their ticket to Brazil 2014.
Despite going down a man six minutes into the second half, Iceland held Croatia to a scoreless draw in Reykjavik to send the play-off into Tuesday's second leg in Zagreb with everything to play for.
European champions Bayern Munich set a new record for the longest unbeaten run in Bundesliga history with a 3-0 victory at home to Augsburg, while Borussia Dortmund went down 2-1 at Wolfsburg.
Mainz missed an opportunity to surpass Bayern Munich at the top of the Bundesliga with a humbling 4-1 defeat at Hanover, while Hamburg beat Eintracht Braunschweig 4-0 and Wolfsburg edged Hertha Berlin 2-0.