Kvitova's victory in the first reverse singles gave the Czechs an insurmountable 3-0 lead in the first-round match and secured a 10th straight appearance in the last four. They will face Germany in the April semifinals. The last time they met, the Czechs defeated the Germans 3-1 in the 2014 final.
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 in the doubles to make the final score 3-1 to the Czechs.
Kvitova, 27, who won Wimbledon in 2011 and 2014, secured the victory against Bencic on her first match point.
"It was better today than yesterday, when I played in the Fed Cup again after such a long time away and needed time to get used to it," she said. "It was a good game from both of us, but I wasn't so nervous as yesterday."
The big-hitting Czech player put her opponent under pressure with aggressive strokes on the indoor hard court at Prague's O2 Arena, breaking serve twice in the opening set.
Kvitova, who hit 10 aces, got the decisive break for a 4-3 lead in the second set after Bencic sent a forehand long.
It was a memorable return to the Fed Cup for Kvitova after she was injured in a knife attack at her home in December 2016.
Kvitova, who won the St. Petersburg Open in Russia earlier this month, was a member of the Czech team that won five of the past seven Fed Cups.
Karolina Pliskova, the Czech No. 1, missed the first-round match against the Swiss because of illness.
In other Fed Cup World Group matches Sunday:
• Tatjana Maria won two points in her first Fed Cup tie in seven years to lead Germany past 2017 finalist Belarus and into the semifinals.
Maria earned her first singles win since 2007 when she won the first reverse singles against Vera Lapko 6-4, 5-7, 6-0. The 19-year-old Lapko made her Fed Cup debut in place of team No. 1 Aliaksandra Sasnovich, who lost her singles match Saturday.
Aryna Sabalenka then tied the match 2-2 by beating German newcomer Antonia Lottner 6-3, 5-7, 6-2. Straight after that two-hour match, Sabalenka returned for the deciding doubles without regular partner Sasnovich.
The Belarusians committed 69 unforced errors as the Germans edged them 6-7 (4), 7-5, 6-4.
• Two-time champion France advanced to the semifinals after beating Belgium 3-2, with Amandine Hesse and Kristina Mladenovic winning 6-4, 2-6, 6-2 against Elise Mertens and Kirsten Flipkens in the deciding doubles match.
Mladenovic double-faulted on her first match point at 40-15 but delivered a strong serve on the next point. It proved enough, sparking wild celebrations from captain Yannick Noah and French staff members at the indoor court in Mouilleron-le-Captif, France.
In the absence of seventh-ranked Caroline Garcia, who is declining to play for France as she focuses on her singles career, the 13th-ranked Mladenovic led the way by winning both her singles matches, including a 6-4, 6-4 victory over Mertens earlier Sunday.
France will play the United States in April. France won the competition in 1997 and 2003 but has lost three times in the final since then, most recently in 2016.