Anderson beat his Serbian opponent 7-6, 5-7 10-6, blasting 17 aces past the world number three.
The Laver Cup is a three-day indoor hard court men's tennis tournament between Team Europe and Team World.
Founded by Federer's management company Team8, in collaboration with Tennis Australia, USTA and Brazilian billionaire Jorge Paulo Lemann, the Laver Cup is a team event inspired by golf's Ryder Cup, and it carries the name of tennis legend Rod Laver.
The format calls for shorter matches.
Team Europe now lead 3-1 with two points up for grabs on day two. In the event of split sets, the third set is a 10-point match tiebreaker. The Bulgarian, Grigor Dimitrov swept aside Frances Tiafoe from the US 6-1, 6-4.
Sock, who came out to warm up wearing a Chicago Bulls jersey over his shirt, fought back and broke Edmund to go up 6-5 in the second set before serving it out as the crowd came alive.
"It's pretty nice to play indoors - no sun, no wind", Dimitrov said.
Four matches remain on Sunday, each worth three points, with doubles to be followed by three singles rubbers.
Roger Federer, Novak Djokovic, Alexander Zverev, Dimitrov, David Goffin and Edmund make up Team Europe. It will be Roger Federer and Novak Djokovic, with 34 Grand Slam singles titles between them. "It's a nice feeling and I think it's great for you guys to see that".
Things were starting to look problematic for Team World after Kyrgios' defeat and John Isner's earlier to Zverev, but Anderson provided a timely tonic to swing some momentum.