Max Dahlin, who was unable to play on Saturday due to an injury, took a 4-0 lead in the first set of the fifth and decisive match.
However, the Swede lost six straight games and ultimately lost his Davis Cup debut 4-6, 4-6 against Wu Tung-Lin.
If they had won against Taiwan, Sweden would have been promoted to the top division, with a chance of qualifying for the playoffs. Now, they face a playoff match in February to stay in the second division.
"We always want to win and belong to the highest division with a chance to make the playoffs. Sometimes it doesn't work out," says Davis Cup captain Simon Aspelin.
