Bremen, who are second and have a 23-match unbeaten streak in all competitions, lacked the creativity of midfielder Mesut Ozil, who was out with influenza.
They carved out only a few chances but hosts Cologne themselves missed clear scoring opportunities.
"We played well until the edge of the box but we just could not finish our attacks," said Bremen coach Thomas Schaaf.
Third-placed Schalke 04, leapfrogged Bayern Munich to join Bremen on 28 points after a 2-0 win over bottom-placed Hertha Berlin which came thanks to Kevin Kuranyi's header in the 59th minute and a stoppage-time penalty by Rafinha.
Kuranyi, battling for a recall to the Germany squad after walking out on them last year, has now scored seven goals this season and is second on the scorers' table.
EARLY SCARE
Bremen had constant trouble feeding striker Hugo Almeida with Marin failing to fill the gap left by Ozil's absence.
