The American came through 6-1 7-6(3) in Geneva to level the score at 1-1 following Dominic Thiem’s earlier dramatic win for Team Europe over Denis Shapovalov.
“We should have won the first match, so we needed to bounce back,” said Team World Captain John McEnroe.
“Jack played awesome, he took it to Fabio. He’s a great ball striker. We feel great right now.”
REPORT: Thiem wins thriller against Shapovalov
Sock had impressed in the first two editions of Laver Cup, racking up a total of 10 points – second only to Roger Federer – but all of them in doubles.
Ranked a lowly 210 in singles after an injury disrupted year, Sock made it onto the 2019 team as a captain’s pick, with McEnroe looking for more from him in the doubles.
For some reason Laver Cup seems to bring the best tennis out of everyone here – Jack Sock
A huge outsider against singles world No.11 Fognini, Sock stunned the Palexpo crowd, and the watching Team Europe bench, as he broke serve twice to take the first set.
Fognini simply could not find his form, letting six break points slip by and making 15 unforced errors in a wayward opening set.
There were supportive words from teammates Federer and Rafael Nadal early in the second but the Italian looked nonplussed, and failed to make the breakthrough as the set headed to a tiebreak.
Again it was Sock who took the initiative, breaking for a 3-2 lead after attacking the net before Fognini handed him three break points with a double fault.
The Italian could only fire a backhand long on the first to spark wild celebrations from the American – and the red bench as Team World enjoyed success in the day-one singles for the first time.
“It’s been a long road back,” said Sock.
“I’m sure everybody here is surprised I won a singles match. I had thumb surgery in February and was out for almost six months.
“For some reason Laver Cup seems to bring the best tennis out of everyone here.
“I’ve played great singles before, so I know it’s in me, but it’s an amazing feeling to bring it out today playing for these guys, not just myself.”
Sock will be back in action on Friday evening alongside Shapovalov as they take on Federer and Alexander Zverev in the doubles.
Taylor Fritz will open for World against Europe’s Stefanos Tsitsipas at 7pm.