Serena Williams overpowered Ukrainian teenager Elina Svitolina 6-2, 6-1 to give the United States a 2-0 lead in the Fed Cup series on Saturday.
In the opening match, American Christina McHale defeated Lesia Tsurenko 6-1, 4-6, 6-3.
The U.S. needs one victory among the reverse singles and doubles on Sunday to return to the top tier of the Fed Cup group.
Williams is making her first Fed Cup appearance on foreign soil in more than a decade to help gain eligibility for the U.S. team at the London Olympics.
The 13-time Grand Slam champion could seal the U.S. win with a victory over Tsurenko on Sunday.
Williams only faltered once against the 17-year-old Svitolina, who managed to reach 2-2 in the first set after going down an early break.
"It's easier in the Fed Cup, as you have a coach who can help and encourage to stay focused," Williams said about U.S. captain Mary Jo Fernandez.
In Fed Cup semifinal play, the Czech Republic leads Italy 2-0, and Russia and Serbia were tied 1-1. The winners advance to the final.
Williams won four straight games and sealed the first set with an ace. There was a short delay while Williams had her ankle wrapped as a precaution, she said.
The 30-year-old Williams pounced on Svitolina's weak serve in the second set and closed out the match in one hour.
The 19-year-old McHale lost the first game in the opener but won six straight to take the first set.
Tsurenko needed a marathon final game in the second set, converting a sixth break point. McHale took a comfortable 3-0 lead in the third set.