Fellow promotion-chasers Fortuna Dusseldorf were beaten 2-1 by Dynamo Dresden to secure Furth's place in the top flight for the first time since the formation of the Bundesliga in 1963.
With three games remaining, Furth are nine points clear of SC Paderborn, who occupy the third and final promotion spot. Furth also hold a vastly superior goal difference of plus-31.
The result leaves Dusseldorf in fourth place in the 2. Bundesliga standings and with no chance of finishing top.
"A dream has come true. We are enormously proud that we have made it," said Furth's sporting director Rachid Azzouzi.
On the night, Zlatko Dedic put Dresden ahead after just seven minutes with Thomas Broeker equalising for the visitors just before the break.
But Dresden were not to be denied as Mickael Pote scored the winner 20 minutes from time to delight the home crowd - and those over 250 miles away in Furth.