He has shown great character in his second appearance at The Open after missing the cut at Turnberry in 2009.
The Kiwi will look to advance further up the leaderboard in the final round alongside former US Open champion Geoff Ogilvy.
Meanwhile, Steven Alker has slipped back at the Midwest Classic on the Web.com Tour.
The 41-year-old, who won the Utah Championship last week to claim his first title in four years, carded an even-par 71 in round three at the Nicklaus Golf Club at Lions Gate in Kansas to drop 32 places to a tie for 39th.
Alker has turned his season around in spectacular fashion. The 41-year-old Hamilton pro, who two weeks ago was 149th on the money list, is currently in 20th place and projected to stay there, after his even-par third round, on the current standings.
His win last week in Utah saw him climb over 200 places on the Official World Golf Rankings and now he is in the frame to qualify for the PGA Tour.
Tim Wilkinson, who has been one of the most consistent players on the second-tier tour so far in 2013, had a three-under par 68 in the third round to drop one place to tied 27th. He is projected to remain in seventh place on the money list.
The Kiwis need to finish inside the top 25 players on the order of merit to automatically qualify for the PGA Tour in 2014.
If all three, including Danny Lee (eighth), can manage that feat it will be a return to the glory days of New Zealand golf. Back in 2002 New Zealand had its best representation on the PGA Tour with five players.
In women's action, world no 1 amateur Lydia Ko has dropped six places in the third round of the Marathon Classic on the LPGA Tour.
The 16-year-old from the Gulf Harbour Country Club carded an even-par 71 in round three at the Hyland Meadows Golf Club to drop from a share of fifth to 11th equal.
The New Zealand women's open champion mixed four birdies with four bogeys in the third round to lose touch with the leaders.
Ko, who is the youngest winner in LPGA Tour history, will begin the final round on a six-under-par total, six shot back from the co-leaders Spain's Beatriz Recari and American Paula Creamer.
The New Zealand rep kept alive her streak of never missing a cut in 22 professional tournaments - a record that goes back to her debut in the New Zealand women's open in 2010.
Following the event in Kansas, Ko will prepare for the British Open at the Home of Golf St Andrews from August 1-4.