Hingis, 36 and a five-time Grand Slam singles champion, was just 17 when she and Switzerland were defeated 3-2 by Spain in the 1998 final.
Hingis won both her singles rubbers in that tie but lost the key doubles alongside Patty Schnyder.
Since then, she has retired and made two comebacks, carving out a successful career as a doubles specialist, even managing to claim a silver medal alongside compatriot Timea Bacsinszky at the Rio Olympics last year.
"In the Fed Cup, I am like the big sister now," admitted Hingis. "My role is different these days but we are a strong team with a great spirit."
Switzerland made the semi-finals by defeating two-time champions France while Belarus shocked the Netherlands despite the continued absence of former world number one Victoria Azarenka who has taken a break from the sport after giving birth to her first child.
The Swiss, playing in back-to-back Fed Cup semi-finals, will start favourites.
Injury-plagued Belinda Bencic is now down at 129 but was as high as seven in February last year.
By contrast, Belarus's top player is Aliaksandra Sasnovich, ranked 96 with Aryna Sabalenka at 125 and Olga Govortsova, contesting her 31st Fed Cup tie, down at 147.
The hosts, however, are on an eight-match winning streak in the Fed Cup.
In Tampa, the United States, winners on 17 occasions, host defending champions Czech Republic who have been winners 10 times -- five in the last six seasons.
The US have not made the final in seven years.
The Czechs, bidding to reach a sixth final in seven years, are missing their four leading singles players, including world number three Karolina Pliskova and two-time Wimbledon champion Petra Kvitova who is recovering from fighting off a knife-wielding intruder in December.
In their place, world number 38 Katerina Siniakova and 109-ranked Denisa Allertova are poised to make their singles debuts in the tournament.
Vondrousova, 17, stunned the sport last weekend when she came through qualifying to win a debut career title at the Biel/Bienne Open in Switzerland despite her humble ranking of 233.
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