With half of the field to return early on Saturday to finish their second rounds, Green went around in a four-under 68 in the morning group to move to eight under for the tournament.
The 2019 Women's PGA champion is three behind leader Miranda Wang (67), who finished with a birdie to move two ahead of Swede Madelene Sagstrom (66).
Green is tied for third with Norwegian Celine Borge (66), Spaniard Azahara Munox (68) and Sei Young Kim (65 ) of Korea.
But it was the Australian's jog all the way to her closing hole - the ninth - with playing partners world No.1 Jeeno Thitikul (seven-under, 68) and Lauren Coughlin (two under, 74) that brought a laugh.
"I don't know who kind of said let's do it. I think it was probably Jeeno, and all of us completely agreed," said Green.
"We were all slowly jogging and Jeeno was going quicker and we're all catching up and all the caddies ran as well. I think if we didn't run on that hole we would still be putting on the ninth green.
"I am just glad it was a team effort and that everyone wanted to finish after already two delays.
"I don't think I could have mentally prepared myself for another delay," Green said with a laugh.
Thitikul, who replaced Nelly Korda atop the world ranking earlier this month, charged into the mix with four birdies on the back nine.
All she wanted to do was finish the ninth after seeing the clouds coming.
"The security guard told us ... three minutes left, so run, ready and go," Thitikul said. "It was start and stop, start and stop. It was frustrating a little bit, but glad we're done."
Green had missed the cut in her last four tournaments and her return to form in Boston must be a welcome relief.
A six-times winner on the LPGA Tour, Green had five birdies with a lone bogey on the third to set herself up for a strong finish at the weekend and perhaps a chance of another win.
When play was stopped, compatriot Minjee Lee was two over after just four holes after finding the par-five second troublesome again where she made bogey - like on Thursday.
Lee has dropped to three-under for the tournament, one ahead of Gabriela Ruffels (71) and Grace Kim (one under after four holes).
The series of rain delays meant leader Wang took some 10 hours to finish her round.
Korda, scheduled for an afternoon start, managed to get in four holes (two birdies) and will return with the second half of the field Saturday morning.
Wang already has 16 birdies over 36 holes and has stretches of big birdie runs. She started the tournament with eight birdies in her opening nine. She finished the second round with three in a row, only it didn't go all that quickly.
She had an eight-foot birdie putt on the par-5 18th when the horn sounded - again - stopping play. Wang returned some two hours later and holed the putt to reach 11-under 133.
with AP
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