The Australian number one carried on from the early work of underdog compatriot Jordan Thompson who stunned Jack Sock in four sets to give the hosts a flying start at a packed Pat Rafter Arena.
In ominous form during last month's U.S. hardcourt swing, Kyrgios blasted 20 aces to Isner's 15, largely defusing the towering American's serve to close out a slow-burning match in two hours and 24 minutes.
Isner battled to the end, saving a match point at 6-5 to take the third set into a tiebreak, then charging into a 5-2 lead. But Kyrgios wrapped up the match in style, mowing through five straight points and sealing victory with a thundering ace.
Hammering a ball into the roaring crowd, Kyrgios hugged captain Lleyton Hewitt and his thrilled team mates.
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"That was unbelievable today," 21-year-old Kyrgios said of the crowd support.
"Obviously I have to take care of my serve (against Isner).
"I've been playing great tennis .. And I returned really well today so I'm really happy to get the win."
Kyrgios gave up only two break points, dropping serve once early in the first set to hand Isner a 3-0 lead.
But the world number 16 Australian stormed back, breaking his opponent to love at 5-5 and serving out the set with an ace.
Another barrage of huge serves saw Kyrgios steal a march in the second set tiebreak and after running the big American all over the court, he grabbed the set with a cheeky drop-shot.
Although there was some carping at the chair umpire and muttering between points, there were no histrionics from the combustible Australian who pushed hard for a quick kill.
He landed a sumptuous cross-court forehand on the line to bring up three break points in the fourth game of the final set but Isner saved them with all.
Lacking his opponent's court speed, Isner swung for the fences and scrapped to within two points of forcing another set, but two fierce returns off the Australian's racquet stole the momentum and set up Kyrgios for his match-winning 20th ace.
Thompson earlier fed off the rowdy home crowd to edge Sock 6-3 3-6 7-6(4) 6-4 for the biggest win of his career.
The 79th-ranked Australian clubbed 14 aces and 17 winners as he ground down the American world number 15.
Wayward Sock sprayed 66 unforced errors and he hammered a forehand wide of the line to give up match point before surrendering the contest with a backhand over the baseline.
Australia are seeking a first Davis Cup title since 2003.
(Reporting by Ian Ransom; Editing by Nick Mulvenney)
