The top-ranked Williams finished off the 66th-ranked Larsson in 66 minutes under the lights.
"I've been through many rain delays so I know what to do," Williams said. "I was back there with the team just trying to stay as fresh as I could."
The winner of the playoff is rewarded with a spot in the 2014 Fed Cup World Group competition. The losing team will play in 2014 World Group II action.
"We're in a good position," U.S. team captain Mary Joe Fernandez said. "Every match is a big match, and looking forward to tomorrow."
Swedish captain Lars-Anders Wahlgren was happy with the tie.
"Of course it's a little bit of a surprise for the Swedish team it's 1-1," Wahlgren said. "I always believe in my girls that I work with. I was hoping for even two-love with a good positive thinking."
Williams dominated Larsson from the outset, posting 31 winners, five aces and scoring on four of five break-point opportunities the Swede offered. Larsson did have three break-point chances in the second set -- two in the first game and one in the third game. Larsson made two unforced forehand errors on her first two break-point chances, and Williams hit a forehand winner on the third.
"I think she played a lot better and I also made more errors in the second set than the first set," Williams said.
The 16th-ranked Stephens was playing her first Fed Cup singles match and was clearly nervous.
"Unfortunate that I didn't get my first Fed Cup live rubber win at this home tie," Stephens said. "But it's OK. Obviously just got to keep pushing and get ready for the next one."
Stephens played a sloppy and rushed match, while the 54th-ranked Arvidsson manipulated Stephens throughout most of the two-hour match. The 29-year-old Arvidsson is playing in her 48th Fed Cup tie and has a 48-35 overall record in Fed Cup competition.
"I was focusing on myself and just trying to play my game," Arvidsson said. "The wind was difficult, but just tried to be aggressive and be the one who hit first."
Stephens acknowledged that Arvidsson's experience was a great benefit for the Swede in the match.
"Definitely tough losing to her," the 20-year-old Stephens said. "At least, I mean, I played someone that really knew what they were doing. Definitely a lot to learn from. Just going into my next tie I'll definitely know what to expect."