British number one Dan Evans produced an inspired display to beat world number 11 David Goffin and level the must-win ATP Cup tie against Belgium.
Evans, ranked 42nd, beat Goffin 6-4 6-4 to leave Jamie Murray and Joe Salisbury with the task of securing victory by winning the doubles later on Sunday.
Earlier, Cameron Norrie lost in two sets to Belgian veteran Steve Darcis.
That meant Evans had to beat Goffin to stop Britain losing the best-of-three tie and exiting the new 24-team event.
Britain lost to Bulgaria in their opening tie on Friday and will be eliminated if Murray and Salisbury lose their rubber against Sander Gille and Joran Vliegen.
The ATP Cup features six groups of four teams, who each play three round-robin ties in an event played across three Australian cities, Sydney, Brisbane and Perth. The six group winners, plus the best two runners-up, will progress to the quarter-finals.
If Belgium beat Britain then they will have won both of their opening two ties, as Bulgaria did following their 2-1 win over Moldova in Sunday's day session in Sydney.
A victory for 24-year-old Norrie against Belgium player-captain Darcis, 35, in the opening match of Sunday's evening session would have given Tim Henman's team a strong platform from which to build on in the tie.
However, he was outclassed by an inspired Darcis - who is set to retire after the upcoming Australian Open - and saw his serve broken twice in each set to lose 6-3 6-4 in one hour and 12 minutes.
Norrie's defeat put the onus on to 29-year-old Evans, who has the game but not always the consistency to match the world's best players.
But he played confidently and cleanly against Goffin, disrupting the Belgian's rhythm, to record one of the most impressive victories of his career.
Evans showed his intent by decisively breaking his opponent's serve in the opening game, and then followed that up with a double break at the start of the second set, which put him into a commanding 3-0 lead.
Goffin responded valiantly in the latter stages as he looked to avoid defeat, claiming one break back in the sixth game and threatening another in what proved to be the final game of the match.
Evans was unable to convert four match points but showed his mental strength by taking his fifth when Goffin dragged a forehand return wide.
"It was real tough out there," said Evans. "We said that he would come at me when it was tight - he's a world-class player. His quality started to show near the end.
The Briton screamed with delight as he leapt in the air in celebration and slapped hands with his team captain Henman, who did an impressive job of ensuring his player remained focused and stuck to their gameplan.
"He did that throughout a long career and there's no-one better to give me a gameplan," Evans added.
"Everybody knows my game is similar to Tim's game. It's great he came out and did this job for us."