Strycova, the world number 33, beat the 52nd-ranked, 19-year-old Kenin 6-7 (5/7), 6-1, 6-4 in two hours and 43 minutes, pulling the Czechs closer to a sixth title out of the last eight editions.
Katerina Siniakova, the world number 31, will face 63rd-ranked Alison Riske in Saturday’s second singles rubber.
The 32-year-old Strycova, who has announced retirement from the Fed Cup after the final, struggled with her serve throughout a nervous first set.
Strycova and Fed Cup debutant Kenin earned two breaks each, with the more aggressive US teenager taking the set in a tie-break.
But, propelled by the sold-out O2 Arena, the four-time Fed Cup winner regained composure in the second to sweep aside the Russian-born Kenin, who is still in search of her maiden WTA singles title.
Strycova took a 5-2 lead in the third and despite giving up two breaks, she took the set 6-4.
“For me it was a lot of emotions,” Strycova said on court after the win.
“I fought every ball and I’m so happy that I could win today in front of such a crowd. It means a lot to me.
“Every point is very important and I’m very happy I could do it today.”
The US are missing Sloane Stephens, Serena Williams, Venus Williams and Madison Keys, while the Czechs are without Karolina Pliskova.
Two-time Wimbledon champion Petra Kvitova has ended up on the bench with a bad cold, although she is hoping to play on Sunday.
The US are the most successful team in Fed Cup history with 18 titles so far, ahead of the Czechs who have won 10 including five as the former Czechoslovakia.