In La Roche sur Yon, France, like Germany two-time winners of the Fed Cup, fought back to 1-1 against Belgium.
Like Serena, Venus is competing as part of Team USA, and won her singles match against Arantxa Rus from the Netherlands, handing the lead to the Americans.
The second reverse singles was not played but Switzerland's Timea Bacsinszky and Jil Teichmann defeated Lucie Safarova and Barbora Strycova 1-6, 6-4, 10-8 to make the final score 3-1 to the Czechs.
Williams will use the match as preparation for her full-fledged return to the WTA circuit at the March 5-18 BNP Paribas Open at Indian Wells before heading to Florida for the Miami Open.
Williams had initially targeted last month's Australian Open for a comeback, but abandoned that ambitious goal after declaring she was not 'where I personally want to be. When I'm too anxious, I lose matches, and I feel like a lot of that anxiety disappeared when Olympia was born, Williams said. "I haven't played a competitive match in quite a few weeks, so I'm definitely not going to be ideal out there, no matter how much I'd like myself to be".
The 36-year-old has not competed in a Fed Cup tie since April 2015 but felt the event was as good as any to start her comeback under the leadership of US captain Kathy Rinaldi.
-France came from behind to even its Fed Cup quarterfinal against Belgium. Karolina Pliskova, the Czech No. 1, missed the first-round match against the Swiss because of illness.
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She hadn't played competitive tennis since winning the 2017 Australian Open while pregnant for her 23rd career Grand Slam singles title, one off Margaret Court's record.
Williams, who gave birth to her daughter last September, lost an exhibition match in Abu Dhabi last December to French Open champion Jelena Ostapenko and later skipped the year's opening grand slam in January due to concerns about her fitness.
"Honestly, I'd like to think CoCo wore her out some", Venus Williams said after her own victory over Hogenkamp. Hogenkamp, bidding to become the 11th Dutch player to record 10 Fed Cup singles match-wins, broke her serve at love.
In front of a roaring home crowd in mountainous Asheville, North Carolina, Venus won the toss and served first, closing out the opening game with a searing ace in an early show of intent. We were pretty tight in the first few games of each set and then when I got the break I felt a little bit better.
After not surrendering a break-point opportunity in the first set, Williams was broken by Rus twice in the second set.
They were level at 2-2 before Venus eventually began to pull away.
The second set was all Williams.
"It's never a win until it's over", she said.