With the top-five set to cash in on additional prizemoney, the season-ending Charles Schwab Cup Championship is taking on added significance.
After the top prize of $A1.5 million, the second to fifth-placed finishers for the season will receive $A750,000, $A450,000, $A300,000 and $A150,000 respectively.
Green currently sits sixth and is chasing a big finish at Phoenix Country Club to enhance his chances.
After his opening 71, Green fired a three-under 68 on Friday to rise nine spots in the field.
The left-hander is now tied ninth, eight shots behind runaway leader Stewart Cink whose five-under 66 gave him a three-shot lead over 67-year-old German veteran Bernhard Langer.
Langer, who has a Champions-record 46 career victories, was second after a 64. He shot his age or better for the 21st time on the tour.
"Every once in a while I look back at my career and have to almost pinch myself and say, 'Man, that's pretty amazing what you've done the last whatever so many years,'" Langer said. "Like a day today, to shoot 64 - three under my age - not a whole lot of people can do that."
The 51-year-old Cink has a 12-under 130 total, shooting a 64 of his own in the first round. The Ally Challenge winner in August in Michigan for his first senior title, Cink entered the week 12th in the season standings.
"It was actually probably a cleaner round than yesterday as far as just my processes and the quality of the shots was probably a little bit better overall." Cink said.
"I just didn't have the hot long putts going in today quite as much, but it was a really solid round. I would love to play golf like that every day."
Langer birdied five of the first seven holes and closed strong with birdies on 17 and 18. He's trying to win at least one event for the 18th consecutive year.
"It's fun to make some putts, that's what the game is all about," Langer said. "If you want to score low, you've got to make some putts."
Alex Cejka was third at seven under after a 66.
Defending champion Steven Alker, second behind Ernie Els in the season standings, was tied for fourth at four under after a 68 - putting himself in position to pass Els for the $US1 million bonus.
Vijay Singh (65), Miguel Angel Jimenez (68), Jerry Kelly (70) and Australian Cameron Percy (68) are also at four under.
Els is at three under after a 70, along with Green, Australian Mark Hensby (69) and Padraig Harrington (69, fourth in year-end standings).
Stephen Ames, third in the standings, is at two under after a 72.
After his opening 69, Queenslander Rod Pampling dropped to 10 places in the field to tied 16th after his second-round 72.
He is one ahead of compatriot Greg Chalmers (69) at one over for the tournament.
The top 36 players on the points list qualified for the event, with Steve Stricker the lone qualifier not in the field. He has never played a postseason tournament on the PGA Tour Champions.
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