The 72-hole tournament is contested with four-ball competitions in the first and third rounds and foursomes in the second and fourth. Italy is the defending champion.
Green and Jones were 5-under over their last five holes Thursday in taking the lead. Pre-tournament favorites Graeme McDowell and Rory McIlroy, from Ireland, and Scots Stephen Gallacher and Martin Laird are tied for the second 9-under.
Green and Jones, playing in the third group off Thursday, jumped into the front with birdies at Nos. 2 and 3 and had another back-to-back birdie run at 7 and 8.
They reached 6-under with an eagle at the 12th-hole, a 531-yard par 5.
The Australians took off with birdies at 14 and 15 and then dropped in an eagle at the par-4, 360-yard 16th. A birdie at 17 got them to 11-under.
The Irish and Scottish teams each had seven birdies and an eagle on the day.