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 could seal the U.S. place in the world group with a victory over Tsurenko on Sunday.
Williams made 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.
In Fed Cup semifinal play Saturday, the Czech Republic leads Italy 2-0, and Russia and Serbia were tied 1-1. The winners advance to the final on Nov. 3-4.
Williams, a 13-time Grand Slam champion, 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.
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.
Was it hard for Williams to maintain focus with such a large lead?
"It's easier in Fed Cup because you have a coach on the sideline to help you and encourage you," Williams said of U.S. captain Mary Jo Fernandez, "and to completely motivate you to stay focused."
The 30-year-old Williams pounced on Svitolina's weak serve in the second set and closed out the match in one hour.
"She has a good game," Williams said of her opponent. "And she's extremely young, so she has plenty of time for (her game) to be even better than what it is."
The 19-year-old McHale lost the first game in the opener but won six straight to take the first set.
"Basically I didn't want to let my team down, and tried to regroup as best as I could to come back," McHale said.
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.
"It was a fantastic start by both Christina and Serena," Fernandez said. "They both really played their game. Christina did a good job to close out her match today. I thought Serena did a good job playing her first match on red clay. "
The U.S. is 18-0 overall when leading 2-0 on the first day of Fed Cup.