Joe Salisbury and Jamie Murray secured a deciding-doubles match for Great Britain against Belgium to win the tie and keep the team alive in the new ATP Cup competition.
Great Britain lost their first round-robin tie to Bulgaria on Friday and faced the prospect of being eliminated at an early stage after going 1-0 down to Belgium in this second round-robin fixture.
Cameron Norrie's loss to Steve Darcis left GB trailing before an inspired victory from Dan Evans over the world No 11 David Goffin levelled the tie.
The new pairing of Salisbury and Murray rose to the occasion and secured the vital 6-3 7-6 (9-7) win over Sander Gille and Joran Vliegen.
Across the course of 10 days, 24 nations are competing in Perth, Brisbane and Sydney. The six winners of each group, plus the two best second-placed finishers across the groups, will make up the final eight.
Great Britain's final tie of the round-robin stage will take place on Tuesday against Moldova.
Salisbury and Murray banished the memories of their hurtful first loss, which saw them squander two match points against Bulgaria in the opening group game.
This time around, the Brits stamped their authority on the deciding match from the outset and it took them just 36 minutes to secure the opening set.
Salisbury, the less experienced of the two men, grew in stature by the second and together the pair used their height and wingspan to dominate at the net.
Neither player made an unforced error during the course of the opening set and they then had to grapple hard in the second.
Gille and Vliegen had re-found their rhythm and serving first, they started to find some gaps to exploit on the court. The pace of the match accelerated and after remaining on serve, a tie-break was needed to decide the set.
Salisbury and Murray fell 3-0 down in the tie-break and then 5-3 before Murray produced a stunning stretch-forehand to swing it back on serve.
The duo then pounced together at the net to bring about a first match point. It came and went with a missed service return from Salisbury, however, he atoned with a storming volley.
The second match point delivered a series of jaw-dropping volleys but again the British pairing let it slip. However, they weren't going to let a third go by and Salisbury's strong return of serve brought about a final error from their opponents and secured the 6-3 7-6 (9-7) victory.
As was the case in Great Britain's first tie, Norrie opened the team's singles matches and from early on it was clear that his 35-year-old opponent was going to be a real handful.
In just the third game, Darcis, who is retiring after the Australian Open, created multiple break-points and eventually converted at the fourth time of asking.
After consolidating his break, the highly experienced Belgium player confidently made it a double-break to press 5-2 in front and took the opening set at the first time of asking on serve.
Darcis then surged 4-0 up in the second set before Norrie started to control the tempo of play more and take the advice of his team bench.
Team captain Tim Henman was asking his charge for 'controlled aggression' and as his first serve percentage raised, the Brit gave his opponent something to think about.
However, Darcis managed Norrie's challenge superbly despite an ill-timed broken string.
His impeccable return of serve, which was a cornerstone of both sets, helped him to remain cool. He held at 4-3 and then had the steel to serve out the clash for an important 6-2 6-4 victory.
Evans arrived on court bursting with energy and instantly made the higher-ranked Goffin know that he was in for a stern test.
The Belgium player struggled with the Brit's variety and tempo and his unforced error count was capitalised upon.
A relaxed Evans raced 5-2 up in the opening set.
The world No 11 responded but Evans stuck to his game plan. He used his sliced backhand to great effect to take the opener 6-4.
Evans broke Goffin's serve at the start of the second set and the British No 1 continued to disrupt his opponent's rhythm and drew gasps from the crowds with some spectacular forehand lobs and passes.
At 5-4 in the 10th game, the British player saw four match points come and go. However, the 29-year-old showed tremendous focus to keep going and get over the line.
A timely ace was followed by another controlled rally and when Goffin pushed the ball wide, Evans roared with delight at securing the 6-4 6-4 victory before watching Salisbury and Murray complete the comeback.
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