Richard Gasquet and Pierre-Hugues Herbert put France, seeking their first title since 2001, in pole position after Saturday's doubles victory, but Goffin quietened a passionate French crowd in Lille to keep Belgium in the hunt for a maiden crown.
"It's been an incredible weekend for me, I've been able to play at a very high level," Goffin told French television. "I gave everything I could and it paid off."
"My work on the court is finished, but my job now is to get behind the team and help support Steve (Darcis)," he added.
Goffin, who outclassed Pouille in Friday's opening rubber, saved a set point while serving at 5-6, as Tsonga was left to rue his inability to capitalise on any of six break points in a marathon first set.
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World number seven Goffin, the runner-up to Grigor Dimitrov at the season-ending ATP Finals in London last weekend, snatched a 75-minute opening set with a blistering backhand return in the tie-break.
Tsonga, who brought France level in Friday's second singles with a crushing win over Darcis, then surrendered his serve in the second set with a costly double fault as Goffin surged 4-2 ahead before seizing a two-set lead.
Darcis, whose most famous win came when he knocked Rafael Nadal out in the first round of Wimbledon four years ago, has five deciding Davis Cup rubber victories in his career.
He beat Australia's Jordan Thompson in the fifth rubber in September's semi-final in Brussels to send Belgium through to a second final in three years.
It is just the third Davis Cup final appearance in the country's history -- after 1904, and 2015 when they lost to Andy Murray's Great Britain in Ghent.
"We've shown that we know how to fight as a team. We've got two great cards to play tomorrow," Van Herck said on Saturday.
France have reached four finals since they last lifted the trophy, with Tsonga and Gasquet both part of the team beaten by a Switzerland featuring Roger Federer and Stan Wawrinka in the 2014 showpiece.
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