The tournament features two-man teams from competing countries. They play two rounds of fourball and two of foursomes. Australians Richard Green and Brendan Jones had an 11-under 63 in Thursday's fourball round but McDowell and McIlroy had their 68 in Friday's foursomes to earn a share of the lead.
Saturday's schedule returns to the fourball format and Sunday's final round is again foursomes.
Australia and Ireland are at 13-under 131 after 36 holes with Scotland, which had a bogey on the final hole, is second at 12-under. New Zealand, Spain and the United States are tied for fourth at 10-under.
Australia also had a final-hole bogey in falling into the tie with Ireland. Green and Jones combined for an eagle, with Green dropping a 10-foot putt on the sixth hole, three birdies and three bogeys for their 70 Friday. Two of the bogeys came in the final four holes.
McDowell and McIlroy had a pair of bogeys but countered that with six birdies.
The Scottish team of Stephen Gallacher and Martin Laird, which had four birdies, was bogey-free until the 18th hole Friday.