Kane's double helped Bayern to a 3-0 win against Lazio in the second-leg of their round of 16 tie, helping them reach the final eight 3-1 on aggregate.
The former Tottenham star later said: "It's a perfect evening for us, a great match. We were down in the first leg 1-0. It was an exceptional performance.
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"The first (goal) is simply about entering the penalty area strong, we talked about it all week. For the second goal I took all the time I needed to finish with the left foot: it was good to see how we constructed the action.
"I think that this was a really important moment of our season. Everyone was watching us, they wanted to see how we would react after the first leg and it was an exceptional performance from everyone. With the ball, without the ball, the energy we brought was was really important."