It was only the club's second win in their last 10 league matches, and came on the back of a 3-1 defeat at Lazio which resulted in elimination from the Europa League last week.
"This is a very important win for us," said Labbadia. "I've got to pay a compliment to the team for the way they managed to shake off the past few weeks and stick to the plan, and now they finally rewarded themselves.
"It was an incredibly intensive game and the way the lads played it proves that they have the right mentality and that they are also fit."
The win lifted Stuttgart away from the bottom three and up to 12th in the table, although their hopes of qualifying for Europe next season still seem to hinge on their DFB-Pokal semi-final against Freiburg rather than their league form.
Frankfurt's hopes of playing in Europe next season are also dwindling with three points in their last six matches, and they still cannot break through the 40-point barrier which they had set themselves as the target at the start of the season.
"This damned 40 points," said their coach Armin Veh to Sky television. "I would have liked to have won and reached 40 points, but we haven't done it."