Skupski (left) and Fleming always looked in control in the Eastbourne sunshine
Great Britain won their doubles rubber against Turkey to claim an unassailable 3-0 lead and prevent relegation to the Davis Cup's lowest tier.
Leading 2-0 after Friday's singles, Colin Fleming and Ken Skupski eased to a 6-3 6-4 6-4 win against Ergun Zorlu and Haluk Akkoyun in Eastbourne.
The victory preserves Britain's Europe/Africa Zone Group II status.
"This job is done but we have to move British tennis forward. This is just a start," said coach Leon Smith.
"It gives you great confidence having that doubles team. You know that on Saturday you've got a great chance of getting a result with these guys."
Turkey's chances were not helped when key player Marsel Ilhan, who lost to Ward in the singles on Saturday, opted to pull out before the game due to mental and physical tiredness.
The 23-year-old was replaced by the inexperienced Ergun Zorlu, boosting the confidence of the British pair, who were already heavy favourites.
Fleming and Skupski, who are nicknamed Flemski and have two ATP World Tour titles, always looked in control, and ultimately stemmed a run of five straight defeats for Britain in the Davis Cup, stretching back three years.
The biggest threat to the British pair early on was a smash from Zorlu that hit Skupski on the side of the head but, although clearly a little shaken, the Liverpudlian was able to continue after a short delay.
And after a break in the eighth game, the first set was easily won by the home pair.
Fleming and Skupski made it four games in a row with another break in the opening game of the second set to take a stranglehold on proceedings.
We felt if we went out there and played to the best of our ability we could get the job done
But, having been utterly dominant on serve in the first set, suddenly Skupski's delivery was under threat and having moved to 0-40, the Turks promptly broke straight back.
More break points came and went for the British pair in the fifth game and they had to wait another four games to break through again.
One break was also all that was required in the third set to seal a success that was Britain's first since September 2007 when they beat Croatia, in Tim Henman's final match, to book a place in the World Group.
Skupski said: "The guys put us in a great position on Friday and we felt if we went out there and played to the best of our ability we could get the job done, and we were able to do that."
Smith could give reserve Alex Ward a chance in Sunday's two dead rubbers, which are reduced to best of three sets, but hinted he was likely to stick with James Ward and Baker.