Harnik scored twice as lowly Stuttgart shocked third-placed Schalke 3-1 at the Mercedes-Benz Arena.
The result boosted Stuttgart's survival hopes, with the 15th-placed side four points above Hamburg, who occupy the relegation play-off spot with three games remaining.
"We were improved at the back today and we were really clinical up front," Harnik said post-game.
"It was important to score the second and third goal when we did as we knew Schalke could always come back. I was happy to score, but the more important thing was the result.
"We realised we could take a big step towards safety. The toughest thing about a relegation battle is staying mentally tough. We managed to do that with the help of the fans."
Huub Stevens' men are now unbeaten in their past three games since tasting back-to-back defeats at the hands of Borussia Dortmund and Nuremberg.
With upcoming fixtures against Hannover, Wolfsburg and Bayern Munich, goalscorer Cacau is determined to lead the club out of their current predicament.
"I've not been in this situation with VfB and I want to do the best I can to help," he said.
"We knew what we could achieve as the other teams lost, but regardless of that, we played really well today. It was a great win.
Meanwhile, midfielder Kevin-Price Boateng lamented defensive lapses that condemned Schalke to their first league loss since March 1 - a run of seven games.
"We made mistakes and they punished us," the former Milan man said.
"The first goal was silly and we went to sleep in the first ten minutes of the second half.
"We've played well in the second half of the season but this is a result we have to move on from quickly."
