On 4 June 1942 during the Battle of Midway Greene was piloting a Douglas SBD Dauntless dive bomber in Bombing Squadron 6 (VB-6) based on the aircraft carrier . He broke through heavy Imperial Japanese Navy fighter and antiaircraft opposition to dive-bomb the aircraft carrier Kaga. Greene survived the attack on the Kaga, ENS Lewis Hopkins said his plane formed up with him on his wing. Eventually Greene's aircraft ran out of fuel and he was forced to ditch in the ocean. He and his gunner were never seen again. Greene was posthumously awarded the Navy Cross. In 1943, the name Eugene A. Greene was assigned to the U.S. Navy destroyer escort USS Eugene A. Greene (DE-549), but its construction was cancelled in 1944 before completion.
