Using microdata of firm exports and international patent activity, we find that Greek innovative exporters, identified by their patent filing activity, have substantially higher export revenues by selling higher quantities rather than charging higher prices. To account for this evidence, we set up a horizontally differentiated product model in which an innovative exporter competes for market share in a destination against many non-innovative rivals. We argue that as the competition among the exporters of the non-innovative product becomes more intense, the innovative firm exports more compared with its non-innovative rivals in more distant markets, a prediction that is empirically confirmed in the dataset for Greek innovative exporters.