The world No.6 defied the windy and smokey conditions at Earl Grey Golf Club in Calgary to post a two-under 70 in the second round of the Canadian Women's Open on Friday.
Green, together with Haeran Ryu (69), is just one behind leader Lauren Coughlin (70) and nicely poised to strike at the weekend before heading off to the Paris showpiece.
Already a two-time winner this year after lifting the Women's World Championship in Singapore in February and the LA Championship in April, the West Australian had to fight hard in her pursuit of the in-form Coughlin.
"It was tough again out there," Green said. "There was some pretty strong wind gusts, especially our last few holes, so committing to the shot you were envisioning was kind of difficult.
"Yeah, I'm kind of glad that I'm finished for Friday and I can go relax now."
Coughlin held onto the lead following her opening four-under 68 to get to six under.
"I think I handled it (conditions) really well overall," Coughlin said. "It was just really difficult to judge how far the ball was going to go with the wind and the crosswind and how firm the greens got.
"And they had some tough pins, especially considering the direction of the wind."
Coughlin is coming off a fourth-place finish two weeks ago in the major Evian Champions. The 31-year-old is still seeking her first win on the LPGA Tour.
Ryu bogeyed the 18th for a 69, in one of the day's best rounds.
"The weather is really bad," Ryu said. "Is a little bit cold and so windy."
The 23-year-old South Korean won the Walmart NW Arkansas Championship last year for her first LPGA Tour title and was second last week in Ohio in the Dana Open.
Three-time champion Lydia Ko had a 71 to join second-ranked Lilia Vu (70) and Jennifer Kupcho (72) at three under. Ko won as an amateur in 2012 at age 15, successfully defended her title as an amateur in 2013 and won as a professional in 2015.
"It's not easy - and I think the scores are showing," Ko said. "Anything kind of under par the past couple days is a really solid round."
Kupcho topped the leaderboard at eight under after birdieing five of the first eight holes in her morning round, then was five over the rest of the way. She had a double bogey on the par-4 16th, four bogeys and a birdie on her final nine holes.
Minjee Lee, who will be joining compatriot Green at the Olympics, had a disappointing 77 to slip down the field at two over in a large group that includes Sarah Kemp.
Overall the Australian contingent will be happy with young West Australian Hira Naveed (71-73) tied 16th at even par, and Robyn Choi (74-71) at one over.
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