Team Europe held an 8-4 advantage after Saturday’s action but their lead was cut to a single point after a thrilling clash opened up proceedings at the O2 on Sunday.
Murray and Berrettini took the opening set but Auger-Aliassime produced a number of sumptuous shots alongside doubles specialist Sock to earn a 2-6 6-3 10-8 victory in one hour and 35 minutes.
It leaves everything to play for ahead of the upcoming singles match between Auger-Aliassime and Novak Djokovic, with John McEnroe’s Team World still holding out hope of winning a maiden Laver Cup title at the fifth time of asking.
Asked on-court if his team believed, Sock insisted: “Hell yeah, why not!
“I was glad I was able to contribute. We got bombarded again first set but we were able to slow things down, turn it around and Felix served excellently.”
Canadian Auger-Aliassime, ranked 13th in the ATP’s singles rankings, was unable to take part in the interview due to the fact he was set to take on seven-time Wimbledon champion Djokovic in the second match.
Team Europe started the third day knowing two more wins would guarantee another Laver Cup success and give Roger Federer the perfect send-off following his emotional final professional match on Friday.
Murray and Berrettini took control immediately and two breaks secured the first set in 31 minutes.
Sock and Auger-Aliassime were able to turn the tables though, with quick reflexes from the latter securing an early break and another forced a 10-point tie-breaker to decide the match.
It was Team World who held their nerve with the pressure on. Murray and Berrettini each served up double-faults before Sock’s excellent drop shot sealed victory for the visitors.
It made the overall score 8-7 to Team Europe, who need Djokovic to be at his best to beat a locked-in Auger-Aliassime.