Williams' win gave the U.S. an unassailable 3-0 lead. Christina McHale later won 7-5, 6-3 against 17-year-old Ukrainian Elina Svitolina to secure a sweep of the singles matches. Americans Liezel Huber and Sloane Stephens completed a 5-0 rout with a 6-4, 6-1 win over 19-year-old twins Lyudmyla and Nadiya Kichenok in doubles.
Williams was making her first Fed Cup appearance on foreign soil in more than a decade to become eligible for the U.S. team at the London Olympics.
"We're back in the World Group where we want to be and it feels really good to get two points," she said.
Tsurenko frustrated Williams early on with accurate hitting from the baseline on the red clay court.
"What's your problem?" Williams roared at herself after hitting two consecutive aces to prevent a break in the sixth game.
The 22-year-old Ukrainian pressured Williams' serve after giving up a break, but couldn't convert two break points. Williams broke again to take the set.
Williams became more relaxed as the match progressed, breaking twice early in the second set.
"I had a little bit of a slow start, but I just knew that I could keep fighting," she said. "I just want to go out there and be super relaxed. I play better when I'm relaxed."
Tsurenko broke Williams to prevent her from serving out the match at 5-1, but the powerful returning of the 13-time Grand Slam champion helped her break for a third time in the set and clinch the win.
McHale's match with Svitolina was tighter. The 19-year-old American broke once to take a close first set, but breezed through the second.