Bayern Munich top scorer Harry Kane struck either side of half-time to steer the Germans to a 3-0 win over Lazio on Tuesday and into the Champions League quarter-finals with an 3-1 aggregate victory, reigniting title hopes among their fans.

Kane headed in for the lead in the 38th minute to cancel out the Lazio's first leg 1-0 advantage and then tapped in their third goal on the rebound in the 66th after Thomas Mueller's first half stoppage time effort had made it 2-0.

The win provides instant relief for coach Thomas Tuchel, who will leave at the end of the season, and his team as they had won just one of their last five matches in all competitions prior to Tuesday and are currently 10 points off the top in the Bundesliga.

"It's a perfect evening for us. It was a big game," said Kane, who has scored six goals for Bayern in the competition and another 27 in the Bundesliga this season.

"We were 1-0 down in the first leg. It's obviously a big moment in our season. It was a top performance.

"Of course we know we have to improve, but nights like this can really change the season. I'm really proud of the boys and we just have to keep this momentum going."

Lazio were on the backfoot from the start and waited to hit the Germans on the break.

Ciro Immobile's header was their best chance but it sailed narrowly wide a minute before Kane bagged his first knockout stage goal in the competition in five years with a diving header.

The Italians, bidding for their first quarter-final spot in 24 years, had succeeded for half an hour in keeping Bayern outside the box but could do nothing when Kane, who had missed an earlier chance, headed in from team mate Raphael Guerreiro's miskick.

Jamal Musiala almost added another seconds later but his sliding shot just missed the target before Thomas Mueller headed in a Matthijs de Ligt volley on the stroke of halftime.

Kane now has 27 Champions League goals, with Wayne Rooney the only Englishman to have scored more in the competition (30).

The former Tottenham Hotspur striker killed off any hopes of an Italian comeback in the 68th, tapping in on the rebound after Leroy Sane's shot was palmed into his path.

The Bavarians refused to step off the gas and Mueller almost scored a second himself but keeper Ivan Provedel tipped his shot onto the post in the 71st.

Bayern have now made it to at least the final eight in 12 of the last 13 campaigns.