The Left party took 6.5 per cent of the vote, exit polls said, further signifying a voter swing to the left.
Should the exit polls bear out, the Left will win seats in Hamburg's legislature for the first time, echoing similar successes in state votes in Hesse and Lower Saxony last month.
As results emerged, the CDU confirmed that they were willing to set up a coalition in Hamburg with the Greens, who took 9.5 per cent of the vote, according to exit polls.
"This gives us the possibility to form a coalition either with the Greens or with the Social Democrats," Roland Pofalla, CDU secretary general, said.
"It is a good result that should be celebrated in Hamburg and in Berlin."
Should Beust decide on a coalition with the Green party, it could persuade Merkel to try a similar method at the federal level in 2009, when she will seek re-election.