The South Americans went close for a second time in the space of a few minutes after some fine work from Juan Guillermo Cuadrado, but Ivory Coast defender Didier Zokora was able to make the interception before Rodriguez could make contact.
After quietening down Colombia's ferocious attacking play, Ivory Coast began to enjoy more possession, but after a sustained spell on the ball Ismael Tiote directed a long-range effort over the crossbar.
However, just before the half-hour mark, Colombia should have gone ahead. The ball was worked into Gutierrez who was waiting in the penalty area, but from eight yards out, the striker volleyed wide.
That was the last chance of a half with few clear-cut chances, but Ivory Coast will arguably be the happier to make it to the break without falling behind.