Björkman was called in at the last minute to deputise for Thomas Johansson, who fell ill on Saturday night. Yet despite putting up a brave show, the 35-year-old Swede found it hard to break Roddick’s serve.
Roddick, 25 and fifth in the ATP rankings, was held to a tie break in the second set, but came back in the third set to win 6-4 over the world number 55.
Roddick’s 6-2, 7-6 (7/3), 6-4 win over the home player in the first of the reverse singles gave Patrick McEnroe’s team an unbeatable 3-1 lead.
The world No.5 won the opening singles on Friday against Joachim Johansson 7-6 (7/4), 7-6 (7/3), 6-3, while Thomas Johansson levelled for the Swedes by beating James Blake 6-4, 6-3, 3-6, 6-3.
On Saturday Bob and Mike Bryan put the visitors ahead again by winning the doubles against Borkman and Simon Aspelin 7-6 (13/11), 6-2, 6-3.
“It’s a big dream come true and I have so much respect for the Swedish team,” said Roddick.
“I think we have the right team to win and I am exited to have the opportunity.”
Roddick always looked to have to much power and pace for Björkman who got the nod from Swedish captain Mats Wilander ahead of Thomas Johansson.
The American comfortably won the first set after breaking serve in the fourth game and it was only in the second that Björkman put up much of the defence taking it to a tie-break in which Roddick jumped out into a decisive 3-0 lead,
There was a sense of inevitability about the third set as Roddick wrapped up the match in two hours two minutes taking his country into the Davis Cup final for the first time since 2004.