The German side were on the back of a horrendous run of form - losing heavily in their last two league matches and going down 2-0 in their opening Champions League game against Chelsea.
But goals from Lars Bender and Michael Ballack sealed a confident boosting win for Leverkusen at BayArena.
Speaking after the match, a delighted and relieved Dutt hailed his side's performance and mentality.
"It was an important victory for us. People talked before the match about how we needed to win, but if you come off a run of three defeats in a row nothing is guaranteed," he was quoted as saying in UEFA.com.
"I saw a good mentality from my team today, even though not everything worked out perfectly, of course."
Despite being pleased with the victory, Dutt admitted there are still room for improvement.
He added: "We sometimes lacked aggression and didn't apply as much pressure as we should have, but that has something to do with the confidence level after the latest results. The victory nevertheless feels great."
The win lifted Leverkusen to second in Group E with three points behind leaders Chelsea.