Nadal, who was earlier shown to have a strapping on his wrist as he watched on the previous matches from bench, expectedly wasn't in shape to play on successive days and chose to opt out.
Roger Federer, who won his first match alongside Alexander Zverev in Friday's doubles tie, beat Australian Kyrgios 6-7 (5/7), 7-5, 10-7 to the delight of his 17,000-strong home crowd.
"So that was something very special for me", the 20-time Grand Slam victor added.
"I saw a real hot chick in the crowd".
Federer and Nadal will join forced to take on Isner and sock, then split up to face Kyrgios and Isner in singles.
Tennis great Rod Laver, for whom the event co-owned by Federer is named, presented the trophy to the Europeans, watched by the world team captained by John McEnroe.
Fritz had earlier put Team World to within touching distance of a shock success with a 7-5, 6-7 (3/7), 10-5 win over Thiem.
"Yesterday, I played and sometimes the next day you are a little bit better, sometimes you are a little bit worse".
Two points are rewarded for each victory on day two of the Laver Cup, compared to just one yesterday, so Isner's victory was enough to bring his team level.
Sock and Kyrgios received 6-Four, Three-6, 10-6 as Crew World minimize Europe's result in 7-5 heading into the ultimate day.
Pegged back, matters looked to be going from bad to worse for Europe when the unsafe Kyrgios took the first set against Federer.
Thiem, ranked fifth in the world, needed only one break to take the opening set but 20-year-old Shapovalov fought back to break twice in the second set to tie at one set apiece. They told me this is how I can turn my season around and get my confidence back.
I was just trying to stay focused.
The European team also won the first two Laver Cup editions, played in 2017 in Prague and previous year in Chicago.
The Laver Cup is a tennis version of golf's Ryder Cup, with Europe winning both editions held so far.