Said Coric, "This is the most special moment of my whole life...by far".
At 1-1 in that contest, Coric was in control when 5-1 up in the third set, but the Americans were dreaming of a come-from-behind victory when Tiafoe rallied to win that set in a breaker.
Croatia, who saw Marin Cilic and Borna Coric both win their singles matches on Friday, will try again on Sunday to book a final date with defending champions France in November.
21-year-old Coric had lost his only previous encounter with the USA number three at Roland Garros but on Zadar's clay courts drew first blood for the hosts against Johnson, who is leading his country in the absence of John Isner and Jack Sock.
Croatia leads the US 2-0 after day one of the Davis Cup semi-finals while France looks in control over Spain in the second tie on Friday.
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The world No. 6 needed two hours and 14 minutes on Friday to give his team a 2-0 lead over the United States in this semi-final tie, which is being played on outdoor clay at the Sportski centar Visnjik venue in this southwestern city, reports Efe.
In the second semi-final at the Stade Pierre-Mauroy, France's Benoit Pair outplaying an injured Pablo Carreno-Busta of Spain 7-5 6-1 6-0 in the opening rubber.
He took a 6-1 lead in the second set tiebreak in superb fashion only to crumble under Querrey's onslaught with the American world number 61 winning seven straight points.
"I just hung in there", said Querrey, who jumped into the arms of USA captain Jim Courier to celebrate. They were two points away from sweeping the Americans 3-0 when Mike Bryan and Ryan Harrison were serving to stay in Saturday's doubles match and trailing 15-30 late in the fifth set.
Meanwhile, Spain won the final day singles matches against France to give the tie a more respectable 3-2 scoreline. "I really wasn't paying attention", Tiafoe said.
"We have good quality and good chances (to win)", he said.