Winning the tournament for the first time since it was declared a major in 2001, Steinhauer ended at 7-under-par 281 for a three-shot victory over Cristie Kerr and 2000 champion Sophie Gustafson.
'I feel like I'm living in a dream,' said Steinhauer, who shot a 66 on Saturday to take the lead overnight. 'I just absolutely am stunned.'
The du Maurier was replaced by the British Open as the fourth women's major in 2001, two years after Steinhauer claimed the second of her back-to-back Women's British titles in 1999.
'People thought that they were a major,' Steinhauer said. 'Now that it really is, now that I've really won it as a major, it makes the other wins that much sweeter, too.'
Despite her record at this event, Steinhauer admitted being more than a little nervous before her final round.
'It's not like I hit it terrible on the driving range, but I didn't hit it very well and I was extremely nervous out there,' she said. 'Like I said, I'm speechless. This is incredible for me.'
Kerr closed with a 71 and Gustafson had a 72 to finish at 4-under 284.
Juli Inkster, who led following the first two rounds, and Lorena Ochoa both shot 73s to share fourth place at 3 under.
Annika Sorenstam, the 2003 winner at Royal Lytham & St. Annes, had a triple-bogey, a double-bogey and two bogeys on the back nine and shot a 7-over 79. She tied for 31st place at plus-7.
'A lot of bad swings,' Sorenstam described her round. 'It just didn't add up. I'm bummed.'
Michelle Wie finished outside the top-five for the first time at a major this season, ending at 6-over to share 26th place.
Wie, 16, carded her third 74 of the week. She also shot 74 in the first two rounds, including Friday when she was assessed a two-shot penalty for grounding her club in a sand trap.
Those two shots ended up only being the difference between 26th and 22nd place.
'I feel like I learned more here this week than I did the whole summer,' said Wie, who tied for third place at Royal Birkdale last year.
Steinhauer's biggest threat Sunday came from Kerr, who was within one shot at 7 under before she bogeyed the par-4 16th when her approach hit the green and rolled off the back.
Kerr also double-bogeyed the 18th to join Gustafson in second place.
As for Steinhauer, slow and steady won the race on a rainy Sunday. She collected one birdie and 16 pars in what was a spotless round until a closing bogey at the 18th, where she knocked her approach into a bunker with a 6-iron.
It was Steinhauer's first bogey since No. 5 in the second round, and came after her caddie informed her she had a four-shot lead -- not two shots, like she believed.
'I think I just kind of went limp at that point,' Steinhauer said. 'I was in shock. I was just kind of sweeping it home. I would have liked to have made a par obviously on the last hole, but I hit a really good bunker shot and just missed the putt.'
Steinhauer's birdie came at the fourth hole, a 371-yard par-4 where she stuck an 8-iron within 10 feet.
Something Steinhauer did well all day was hit consistent iron shots. She'll have to do the same thing next year when she defends her title at St. Andrews.
'Looking forward to it,' Steinhauer said.
Lorie Kane shot a 70 and Beth Daniel a 72 to tie for sixth place at 2-under 286. Julieta Granada was eighth at 1 under, while Ai Miyazato carded the round of the day with a 67 to finish at even-par and in 10th place.