Steinhauer, the 2006 Women's British Open winner, was at 12-under 204 for a one-shot lead on Rachel Hetherington. There were eight players within five shots heading into the final round.
Hetherington had a 5-under 67 to stand at 11-under 205.
Michele Redman fired the round of the day, an 8-under 64, to share third place with Christina Kim (71) at 10-under 206.
Sorenstam, playing for the first time in three weeks and looking for her first win since claiming this title last year, shot 71 to stay in the mix at 9-under 207, three strokes back.
Becky Morgan was also at 207 following a 69.
'The round kept me in there and that's been the hardest part this year is putting together four solid rounds,' said Sorenstam. 'I've had a tough time. I'm looking forward to tomorrow and hopefully posting a low round.'
Steinhauer failed to break 70 for the first time in three rounds, making it around Panther Creek on Saturday with just three birdies and two bogeys.
She went 2 over par on her first 12 holes, three-putting for bogey from 40 feet at the second hole and two-putting from 8 feet for another bogey at the 10th.
But Steinhauer saved her lead with three birdies on the next four holes. She knocked a pitching wedge to eight feet at the 13th, drove a 9-wood to 12 feet at the par-3 14th, and two-putted for birdie from 30 feet at the 16th.
'I feel really fortunate with the finish,' said Steinhauer, who owns seven career LPGA Tour wins. 'I got off to a very slow start today. Actually I feel like I hit the ball as well as the first two days, but through the first ten holes, nothing.
'I didn't have any putts fall and just wasn't feeling quite as comfortable. Just feel really fortunate that I made three birdies on the back nine to come back and shoot 1 under today.'
Hetherington, the eight-time LPGA winner, collected five birdies for her 67.
'I hit the ball really solid today and I putted well. And when I needed to, I chipped well,' said Hetherington, who couldn't remember the last time she was in this position.
'At least 2003, I would say,' she guessed.
Redman's 64 was three shots better than the closest player and one stroke off a career best. Her eight birdies included three straight putts longer than 20 feet: at the eighth, 11th and 12th holes.
Redman's two LPGA Tour wins came in 1997 and 2000.
'I knew I was playing well,' she said. 'Even the first day when I shot one- over, you know, I knew I was playing well ... Today was nice. Today was probably something that I needed for myself, so whatever happens tomorrow (Sunday), I'm OK with.'
Sorenstam had three birdies and two bogeys on Saturday, including a birdie at the par-5 16th, which she has played 4 under par through three rounds.
With new No. 1 Lorena Ochoa out of the picture this week -- the Mexican star is taking a one-month break -- Sorenstam has an opportunity to regain some of the spotlight she's lost to Ochoa over the last year and a half.
'I didn't give too much room to the leaders and I'm still right there for Sunday,' said Sorenstam.