And while they reached different conclusions Friday, they wound up in the same position atop the leaderboard.
Ochoa recovered from a double bogey that could have been worse with back-to-back birdies, including one on the 18th in the middle of her round. From 192 yards away, it wasn't a question of going for the green, only which club to use.
She wanted a 7-wood. Her caddie suggested a 5-wood, and it's a good thing Ochoa listened to him. Her approach landed 5 feet over the water and hung on the bank, from where she chipped to 8 feet for birdie.
'He saved me,' Ochoa said after a 1-under 71. 'The ball would be under water right now.'
Creamer played splendidly, a bogey-free round of 67 in which her longest putt for par was 4 feet. She had a chance to take her first outright lead in a major when she had 210 yards to the 18th green, her final hole.
She also listened to her caddie, who suggested she lay up.
'I'm a pretty aggressive player,' she said. 'If I needed to do it, I would have done it. But it's only Friday.'
They wound up at 4-under 140 on a tough Mission Hills course that is so firm and fast it has refused to yield the kind of round Ochoa had last year, when she opened with a 62 to tie an LPGA major championship record.
'I think they wanted to not keep it soft for us so we don't shoot so many low under,' she said with a laugh. 'They're blaming it on me.'
Suzann Pettersen of Norway, a runner-up to Ochoa last week outside Phoenix, shot 69 and joined Shi Hyun Ahn (73) at 141.
Another shot behind was Se Ri Pak, who needs a victory this week to become only the seventh woman to complete the career Grand Slam. She made 14 pars on her way to a 70 that finally gave her a decent chance at a Mission Hills course that has tormented her.
Missing from the mix, by a mile, was Annika Sorenstam.
The world's No. 1 player -- but maybe not for long if Ochoa wins this week -- was coming off her worst start at a major in seven years when she opened with a 75. She added another dubious footnote to her record on Friday with only one birdie in a round of 76, making it her highest 36-hole start at a major since she went 76-75 at Oakmont in the 1992 U.S. Women's Open. She was an amateur that year.
'It's just not happening at all,' Sorenstam said. 'I'm very disappointed with the outcome, obviously. I'm doing the best I can.'
Only nine players remained under par.
Mission Hills played even tougher than the first round, even on another day of sunshine in the Coachella Valley with barely a breeze. The greens were firm as ever, but what cost Ochoa in the early going was the thick grass framing the fairways.
Her tee shot on the 15th sailed right into the rough and under the trees, and she tried to scoot a 4-iron up the fairway. But she topped it slightly, the ball never got much air under it and traveled a mere 15 yards, still in the rough, still slightly blocked by trees. Her third shot hung up on a steep, grassy lip of the bunker, and her chip ran through the green into more rough.
Ochoa chipped to 4 feet and holed the putt to limit the damage. And while she lost two shots, she kept her perspective.
'I saw myself under par,' said Ochoa, who at that point was 1 under. 'And under par is always a good score in a major.'
She steadied herself with a tee shot into 18 inches on the par-3 17th, a tough hole with a front pin and hard green. And her round turned on the par-5 18th, which played 485 yards to give players a chance to reach the peninsula green in two.
But the rest of the round wasn't smooth sailing for the 25-year-old Mexican star.
From the right rough on No. 1, she punched out over a cardboard trash can and just onto the green, but then knocked her 40-foot birdie attempt about 10 feet by and caught the lip for a three-putt bogey. She came up well short with a wedge on the par-5 second, and left herself a testy 6-footer for par. She made that to avoid consecutive three-putts, then spent the next two holes standing over 4-foot par putts that she made to keep momentum on her side.
'Those were the key,' Ochoa said. 'That really changed, just making them, giving me relief and I kept myself in good position.'
Creamer was in great position all day.
The longest of her five birdie putts was 10 feet on the 12th, and she missed four other birdies from inside 12 feet. So the 20-year-old American turned into a prophet, for even after a 73 in the opening round, she said a low score was out there at Mission Hills.
'I gave myself a lot of chances, and we'll take it,' she said. 'But two more days left. That's a lot of golf.'
Creamer spent the first two days with Sorenstam, the world's No. 1 player, and now gets Sorenstam's heir apparent.
'Annika right now is the world's No. 1 player,' Creamer said. 'Lorena is playing unbelievable.'
The season-ending ADT Championship will return to Trump International in West Palm Beach, Fla., for the next two years. ... Stacy Lewis, who plays college golf at Arkansas, shot a 73 and was the low amateur at even-par 144. ... In her first tournament since August because of bone spurs on her right foot, Meg Mallon birdied the last hole and made the cut by one. ... Karrie Webb, the defending champion, made four straight bogeys and shot 77.