Roberto Firmino opened the scoring in the eighth minute, but Zoltan Stieber levelled before half time.
Joselu put Hoffenheim in front for the second time in the 67th minute, but Edgar Prib replied in the 84th minute before Joselu thought he had earned the home team all three points five minutes later.
However, Germany Under-21 international Lasse Sobiech equalised again with the last touch of the game as Furth picked up their fifth point of the season on their travels.
Furth's previous four points had all been picked up away from home and they showed precisely why they have been more comfortable on their travels with Edu firing wide early on.
Sercan Sararer then wasted another good chance for Mike Buskens' side before Hoffenheim drew first blood with their very first attack.
Firmino was left with too much room to meet Sebastian Rudy's free-kick and head in from close range.
The goal gave Hoffenheim more confidence and stifled Furth's early enthusiasm, but the visitors recovered well to find a deserved equaliser five minutes before the interval.
Tim Wiese, back in the Hoffenheim goal despite conceding 15 goals in four games prior to picking up a groin injury, had to pick the ball out of the back of the net again after only parrying Prib's shot out for Stieber to equalise.
Andreas Beck squandered a good chance to restore Hoffenheim's lead early in the second half with a weak shot causing Max Grun no problems in the Furth goal.
Kevin Volland failed to capitalise on a slip by Grun, but the chances were starting to arrive with a greater frequency for Hoffenheim.
They took the lead midway through the second half with Volland showing he is better at setting up goals than scoring them, sending a perfectly-weighted pass through for Joselu, who beat Grun in a one on one.
Vincenzo Grifo came on for his Hoffenheim debut and almost marked it with a goal which would have earned Hoffenheim the points, but his volley was pushed on to the bar by Grun.
Prib brought Furth back level in the 84th minute with a precise shot past Wiese from just outside the penalty area, but there was still time for Hoffenheim to score again.
It was the same combination as for their second goal with Volland threading the ball through for Joselu, who this time needed two chances to beat Grun.
Hoffenheim were preparing to celebrate a return to winning ways when they conceded a corner just before the referee blew for time, and there was just enough time to finish off the last attack of the game, which Furth did effectively.
Sobiech met Stieber's corner at the near post and beat Wiese with a header into the far post, sparking scenes of celebration on the Furth bench with coach Buskens racing on to the field as the final whistle sounded.