Kiessling's penalty, which made him the league's outright top goalscorer on 16, and a Lars Bender header late on turned the game around, but the German striker said it would have been a travesty had they not won.
"I think everybody could see how deep Stuttgart were," he said
"They had every man and mouse packed into their own penalty area and that made it hard for us.
"We altered things in the second half and attacked a lot better, creating more chances.
"I cannot remember having to go back and defend even once, and I think that shows how deserved the win was today [Saturday]."
Kiessling praised his team mates for never giving up, even as the minutes ticked away, as Leverkusen opened up a seven-point cushion over fourth-placed Eintracht Frankfurt in the chase for an automatic place in the Champions League next season.
"It's absolutely fantastic when you see the morale of this team," he told Sky television. "We never gave up.
"Of course it's bitter when you concede a goal due to a mistake, but that's football and we turned it around, and it was a thoroughly deserved win today [Saturday]."