The Americans had been 2-0 up after singles wins on Friday, but Williams succumbed to a 7-6 3-6 7-6 loss to Anastasija Sevastova, while Kenin was beaten by Jelena Ostapenko.
But victory for doubles duo Kenin and Bethanie Mattek-Sands in the deciding rubber secured the Americans a spot in April's Finals in Budapest.
Fed Cup Singles
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17/04/2021 AT 17:16
Australian Open champion Kenin rarely looked comfortable against a fired-up Ostapenko, and despite a brief revival in the second set, it was the Latvian who took it relatively comfortably in the third set, 6-3 2-6 6-2.
Williams was the favourite against Sevastova in her second singles matches, but hit 30 unforced errors in a shambolic first set before being edged out in a dramatic third set tie-break.
The USA had their doubles pairing to thank as Kenin and Mattek-Sands made short work of the deciding match, winning 6-4 6-0 in an encounter that lasted little more than an hour.
America will be joined at the Finals by Spain, Russia, Germany, Belarus, Switzerland, Belgium, Slovakia, Australia, France, Czech Republic and hosts Hungary.
Fed Cup Singles
Boulter, Watson win to put GB in command against Mexico
16/04/2021 AT 16:38
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Fed Cup finals and play-offs postponed
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