He struggled to stay with Sock in the opening set but seized his chance when the American's serve deserted him at 3-4, breaking Sock to win the opener in 37 minutes.
U.S. pair Steve Johnson and Jack Sock kept the Davis Cup quarter-final against Australia alive with a gritty five-set win over John Peers and Sam Groth in Brisbane on Saturday.
Thompson's first serve velocity averaged out at 190kmh through the first three sets, with his fastest ball clocking 222kmh, and he moved eagerly at the back of the court.
The two countries have 60 Davis Cup titles between them but Australia have not won since they bagged their 28th crown in 2003, while the USA snared their 32nd a decade ago.
Former Australian tennis player Todd Woodbridge says that Nick Kyrgios' game has a taken a positive step forward.
Quarterfinals: At Brisbane: Australia 2 leads US 0 [Jordan Thompson bt Jack Sock 6-3, 3-6, 7-6 (4), 6-4; Nick Kyrgios bt John Isner 7-5, 7-6 (5), 7-6 (5)].
"Right now, a lot of people could argue he's playing maybe the best tennis he's ever played", the 23rd-ranked Isner said.
Sock and Johnson battled from a set down to claim the second set and then claimed a 4-0 lead in set three.
One more win will send Australia through to a semi-final date with Belgium or Italy in September.
7/4/17 Australia's Jordan Thompson reacts after winning a point against Jack Sock of the US during their Davis Cup quarter-final match.
Thompson, playing only his second Davis Cup tie, went into the match against the American number one as the huge underdog.
Australia's Sam Groth and John Peers are not low-ranked journeymen, as was the Swiss team Adrien Bossel and Henri Laaksonen.
"It feels obviously refreshing to have a challenge in front of us", American Captian Jim Courier said. "I don't get too nervous or wound up too badly, but there is a little extra pressure".
The 79th-ranked Thompson won both of his singles in his Davis Cup debut against the Czech Republic in February, but he was more impressive against No. 15 Sock, the highest-ranked player in the quarterfinal.
Kyrgios had some great outings during his recent great stretch, defeating world number two Novak Djokovic in straight-sets at Acapulco and Indian Wells. That liability has turned into an enormous advantage, because all four US players (John Isner, Sock, Querrey an Johnson) are accomplished in singles as well as doubles.