Siniakova wasted a 3-0 lead in the final set and the 19-year-old Kenin, who was playing her second match in her debut Fed Cup tie, fought back.
Siniakova, the world number 31, then saw off 63rd-ranked Riske 6-3, 7-6 (7/2).
The two most successful teams in the tournament's history were facing off without their top players.
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The Czech women's tennis team won Fed Cup for the first time in 2011 after the country's independence in 1993.
Petra Kvitova has been ruled out of the opening day of the Fed Cup final because of illness. A home player made a great recovery in the second set, fending off all six break points she faced in three straight games and earning breaks in games two and six before closing it with a service victor at 5-1 to gain the momentum and gain an even bigger support from the stands. "I think I definitely do like the court a lot and any time that I'm indoors".
"It was an incredible game for me, up and down, lots of nerves", Siniakova said.
"Every point is very important and I'm very happy I could do it today".
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"I was pretty nervous but I was able to handle it", she said. "I believe in all my players up here", she said.
The second set may have ended 6-1 - a relatively one-sided scoreline, but the process for Strycova to level the match was way harder than you thought.
Siniakova, who won the French Open and Wimbledon doubles titles with her Czech team mate Barbora Krejcikova this season, proved too much in the end for the Russian-born Kenin, who cried after the match and was consoled by her team mates.
An eventful opener set the tone as the two players combined for seven breaks of serve, Siniakova finally taking it in the 12th game on her third set-point opportunity. "We'll see what happens - we're prepared, we're ready to go".
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The inexperienced U.S. team are without Serena and Venus Williams as well as Sloane Stephens and Madison Keys, while the hosts have Karolina Pliskova injured. Riske pushed the set to a tiebreak, where Siniakova took control.