Steinhauer and Laura Diaz combined for a 4-and-2 upset over Sorenstam and Catriona Matthew to help the Americans to a 2 1/2 -1 1/2 lead after the alternate-shot matches Friday morning.
Gwladys Nocera and Maria Hjorth defeated Natalie Gulbis and Morgan Pressel 3 and 2 for Europe's lone victory.
Suzann Pettersen and Sophie Gustafson salvaged a tie for Europe against Cristie Kerr and Pat Hurst -- something of a victory, really, considering the Europeans played most of their match from behind trees and in the rough.
The Americans are seeking to win the cup in Europe for the first time since 1996 and they were off to a promising start. This marked the first time the United States had won the opening fourball matches since 1998.
'It's hard to put into words because we've struggled so much in this format,' said Diaz, who earned her first career point in foursomes.
Players took a short break, then went back out for best-ball matches in the afternoon at Halmstad Golf Club, where the weather was miserable -- with wind, heavy rain and temperatures in the 50s that had the players reaching for both their umbrellas and their stocking caps.
None of that seemed to bother Steinhauer, who missed a 3-foot putt on No. 10 to bring a match the Americans had led by two back to all-square.
From there, she was simply terrific. After the Americans regained the lead on No. 11, Steinhauer saved par from 8 feet to halve No. 12, then hit her tee shot on the par-3 13th to near tap-in range to go 2 up.
On No. 14, Matthew hit her approach shot to 6 inches, putting herself and Sorenstam in line to trim the lead. That's when Steinhauer, who works with a long putter, knocked in a 20 footer to halve the hole and suck away whatever momentum the Europeans may have felt moments earlier.
'I have a long time in my career, and it's been rejuvenated, and to be back, it's unbelievable,' said Steinhauer, the 44-year-old who is back at the Solheim Cup for the first time since 2000.
In the match behind them, Inkster and Creamer were leaking oil, having blown a 2-up lead and looking like their match might be settled on the 18th. But Davies hit her tee shot on the par-3 16th into the water, then hit a bad approach on 17 that forced Brewerton to simply punch out from behind a walking path. The Euros conceded the match on the 17th green.
Europe's half-point from Pettersen and Gustafson was something of a bonus considering they found basically every patch of trouble on this long, but not overly narrow, Swedish golf course.
Trouble began on the first tee box when Pettersen, the reigning McDonalds LPGA champion, yanked her shot behind a tree on the left side.
The scrambling began and didn't end until the very end, when Gustafson, playing from a thin lie in some trampled-down rough, got the ball to about 15 feet on No. 18. Kerr played her approach from the fairway, but yanked it left.
Pettersen had a chance to win, but left her putt a tad short. Hurst, meanwhile, chipped to about 8 feet, and Kerr actually had to make a tester to salvage the tie -- the first time the Americans weren't in control of the match all day.
In the final match, Nocera and Hjorth were in command pretty much from the beginning as the two young Americans had trouble harnessing their game. Pressel lipped out a short putt on No. 4 that would've won the hole. Gulbis missed a 6-footer on No. 6, then another on No. 12, as the Americans finished 16 holes in 4-over par.