He defeated Andrei Rybalko, ranked 350th in the world, 7-5, 6-3, 6-3, to ensure Britain's place in the First Division of the zone after Tim Henman had suffered a four-set defeat against Andrei Medvedev.
"I was a little nervous at the start, but I might have won my match even before it began," he said. "I gave the guy a straight look as we tossed for ends and it seemed as though the psychology worked.
"There is probably even more pressure in these ties than playing at Wimbledon because when you come on last with the scores level, you know you must not let your country or your team-mates down. Happily, I didn't do that.
"It's a pity we have had to play this match to avoid a relegation problem, but from here on in we all want to make sure it is up and up all the way."
Without ever showing the form he displayed in reaching the Wimbledon quarter-finals, the left-handed Rusedski, 24th in the world, still did enough to spare any further British embarrassment in the competition. They will not now have to play Hungary in September.
Earlier, the usually mild-mannered Henman again lost his temper as he was overcome 6-7, 6-3, 6-4, 6-4 by the higher-ranked Medvedev. The British No 1 was warned for swearing just 48 hours after being called for an "audible obscenity" in his opening five-set game with Rybalko.
The flashpoint came when Henman, serving to save a break at 6-5, thought he heard a let call when the umpire ruled out his first service. After a long argument, he strode away and the warning was then given for another comment, before a poor backhand allowed Medvedev to force the set into a tie-break.
"Tim was into Davis Cup as strongly as ever and I thought Greg was absolutely superb today, considering the pressure that was on him," David Lloyd, the Great Britain team captain, said. "Some people would have blamed him if it had gone wrong because Tim had already beaten Rybalko, who looked a much better player than his ranking suggests. On clay, for sure, he would give most top 20 players a good test."
Henman and Rusedski's scintillating doubles debut success against Medvedev and Dmitri Poliakov on Saturday always had Britain in the driving seat for the final session and it was just a case of Rusedski steering them home on the last lap.
His service was never quite as intimidating as on grass, but was certainly enough to keep Rybalko on the back foot, even though the Ukrainian took advantage of consecutive double-faults to get a break in the opening game of the second set.
Mark Petchey was beaten in the final of the Bristol Challenger Trophy at Redland Green yesterday. Petchey, the top seed, lost 7-6, 7-6 to the Italian Stefano Pescosolido in a rain-interrupted final lasting 1hr 40min.Reuse content