Storm shot an 8-under 64 and Green shot a 65 to share the lead at 11-under 133.
Twenty-seven players still need to finish their rounds after a backlog from Thursdays opening round, which was called because of rain and darkness. The cut is expected to be at 2 under.
Englands Paul Casey (65) and Anthony Wall (67) were one shot back. Northern Ireland teenager Rory McIlroy (69), Brett Rumford of Australia (67) and Johan Edfors of Sweden (69) were two shots behind the leaders.
Padraig Harrington of Ireland (66) was tied for 10th place and Sergio Garcia of Spain (71) was eight shots back.
Storm had an eagle, seven birdies and a bogey. He was paired with Green, who tore up the front nine with six birdies.
We always seem to play well together and the last time we played together, he won the Australian Open, Storm said