Power birdied two of the last three holes to shoot five-under 67 while Poston made double bogey at the par-5 15th and a bogey at the par-3 16th to stumble into the playoff with a 70
The 28-year-old American dubbed it "another good day" at Wilshire Country Club, where she followed up a course record-equalling 64 with a largely stress-free, steady round.
8 Both US events will have a field of 144 players with Canada's Brooke Henderson seeking a third consecutive Lotte win after last year's cancelation. South Korean Lee Min-jee is set to try and repeat in LA after her 2019 win and a 2020 wipeout.
"I think at my stage of my career there's not a lot a caddie can tell me. But, obviously, Helen gets me in a fantastic mood out there. Psychologically, she can help me and say the things that I need to hear."
Spieth has had his troubles off the tee in the Arizona desert, hitting just 43% of fairways, but he has hit 80% of greens in regulation and on Saturday he made the most of his chances.
Casey recorded six birdies and capped off his day with an eagle on the par-five 18th in an error-free round to jump up five places to lead Scotland's Robert MacIntyre.
To finish off with an eagle was pretty cool," Casey said. "You can never say (the round was) flawless...
The leading duo were one stroke in front of reigning Rookie of the Year Scottie Scheffler, whose seven-under 65 on the North Course included holing out for an eagle two at the par-four 16th.