The 21-year-old levelled the Group D tie with a 6-7 (3/7), 7-6 (12/10), 7-5 win over the world number 19 in two hours and 43 minutes.
He saved two match points in the second set and weathered 33 aces from Isner, after Taylor Fritz thrashed Viktor Durasovic 6-2, 6-2 in the opening match in Perth.
Ruud then backed up in the decisive doubles alongside Durasovic to down Rajeev Ram and Austin Krajicek 4-6, 6-3, 10-5 and trigger jubilant scenes from the Norwegian contingent, who were the last team to qualify for the 24-nation event which is also being played in Brisbane and Sydney.
“I didn’t have much time to recover from my singles,” Ruud said. “I was a little bit low (on energy) but I got the feet going and we played great. The players are super proud to beat the US.”
The world number 54 has risen up the rankings over the past year since training alongside Rafael Nadal at the world number one’s academy in Mallorca.
Ruud, whose father Christian is Norway’s captain, clawed back into the singles match and stormed out to a 6-4 lead in the second set tiebreak, but was thwarted on his set points by a desperate Isner.
He saved two match points in a see-sawing set before finally converting on his fifth attempt to keep Norway alive.
It appeared the match was going the distance in the third set until an inspired Ruud broke in the 12th game to clinch his first victory over a top-20 ranked player.
Earlier, world number 32 Fritz gave heavily favoured United States the perfect start with a commanding victory over Durasovic in 61 minutes.
“For the first match of the year, I played really well,” the 22-year-old said. “Last year was my breakthrough, but I always put pressure on myself to do well.”
Fritz — ranked 300 places higher than his opponent — unleashed his big serve with 11 aces and returned accurately to underline the gulf in rankings.
The match was played under the roof due to unusually cool and damp morning conditions in Perth.
The new tournament replaced the Hopman Cup, a popular annual mixed-teams fixture in Perth for three decades.
Russia face Italy in the second Group D tie later Friday.