Earlier on Saturday, Isner fought back from a set down to beat Zverev 6-7 (2/7), 6-4, 10-1 and haul Team World level at 3-3 after Europe led by two points after the opening day.
A year ago in Chicago, Alexander Zverev pulled out the last win for Team Europe by besting Kevin Anderson.
Greek Tsitsipas, ranked seventh in the world, kicked off the evening session with a 6-2 1-6 10-7 win over American Taylor Fritz, claiming the opening set in 24 minutes with two breaks of serve.
But he hit back to level the match with a break in game 11 of the second set, before holding off a late Kyrgios rally in the super tie-break to take it on his third match point.
But despite the stakes on Saturday being higher, with every match now worth two points, Kyrgios found himself bizarrely distracted by a spectator - much to the bemusement of his support team.
"I feel very lucky", said Nadal.
The two-time French Open runner-up recovered from 9-7 down in a super tie-break to win 6-4, 5-7, 13-11 against Canadian youngster Shapovalov.
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They both served well in the remaining six games to set up a tie break where Nadal had the leading role, taking it 7-1 with three mini-breaks to seal the deal and send his team 7-3 in front, with five more matches left to be played.
"It's a really special thing with the tie-break in the third, it creates lots of close moments and match points on either side", Thiem said.
Federer and Rafa Nadal, with a total of 39 Grand Slams between them, gave Fognini plenty of advice during breaks in play as the second set went with serve until the tiebreak.
"Maybe we're turning the tables just a little bit", Isner said.
Kyrgios and Jack Sock won that match 6-4, 3-6, 10-6, scoring two key points for the world team which trails Europe 7-5 ahead of the final four matches Sunday.
The Laver Cup is into its third year but this is the first time the tournament is an officially sanctioned ATP Tour event.
Day two of the three-day tournament awards two points per win, with the first team to reach 13 points declared the victor.