Boateng opened scoring with low shot from 25 yards, Gomez poked in second
Draxler hooked in third from close range
Ozil had penalty saved in 13th minute
Germany will face Italy or Spain in quarter-finals
Germany 3-0 Slovakia
On comes Schweiny.
Bastian Schweinsteiger replaces Sami Khedria for Germany.
Speaking of Lothar Matthaus, Schweinsteiger has now matched the great midfielder's number of major tournament appearances - 36.
Miroslav Klose is the only German with more, with 37.
Image source, EPAGermany 3-0 Slovakia
Mats Hummels goes on a Lothar Matthaus-esque burst from central defence to the edge of the Slovak area. It comes to nothing, but a joy to see nonetheless.
Germany 3-0 Slovakia
It's over 20 years since Germany last won a game at the Euros by more than two goals.
Russia were the unfortunate lot who got whacked 3-0 at Old Trafford on 16 June 1996. Could this side go one further today?
Image source, PAGermany 3-0 Slovakia
Massive round of applause for German fan favourite Lukas Podolski as he comes on. Benedikt Howedes is also off the bench.
Jerome Boateng goes off - he had a calf problem this week remember. But what a luxury, resting your centre-half.
And my man of the match Julian Draxler is taken off too.
Germany 3-0 Slovakia
Yup, they've tried. It didn't go very well, but they tried.
The saddest thing about Slovakia going out is that we lose a player named Norbert from the tournament.
These things should not be overlooked.
Germany 3-0 Slovakia
Pat Nevin
Ex-Chelsea winger on BBC Radio 5 live
It has been a very entertaining and enjoyable game, Slovakia tried to have a go in the second half but it has not helped, at least they tried.
Image source, Getty ImagesGermany 3-0 Slovakia
Slovakia need to do something, so they bring on Stanislav Sestak.
He is immediately tackled by Mats Hummels, who puts in a clean, crisp sliding tackle.
The Polish referee decides it's not only a free-kick, but also a booking for Hummels. Totally odd.
Jan Durica takes the set-piece, 25 yards out, but rattles the effort wide.
Germany 3-0 Slovakia
Pat Nevin
Ex-Chelsea winger on BBC Radio 5 live
We will agree Julian Draxler deserves that goal, it happened in slow motion.
It is a beautiful volley, he took it quite high. Left foot, right foot, it makes no difference, with such comfort, ease and confidence into the top corner.
Image source, Getty Images
(Draxler)
And Germany punish the Slovaks for not upping the tempo.
It comes from a corner, Toni Kroos putting it in. Mats Hummels wins a header that spins off a defender - Julian Draxler, on the left of the six-yard box, watches it drop out of the sky and leathers a volley into the roof of the net.
The boy deserved that.
Image source, Getty ImagesGermany 2-0 Slovakia
Slovakia may have pushed a bit further forward, but they're still allowing Germany loads of time on the ball in their own half. Very little pressing.
Germany 2-0 Slovakia
Julian Draxler is having his own little party - and we're all invited.
He looks like he's absolutely done two Slovak defenders with a tremendous pirouette. Peter Pekarik has to haul him down, but the referee says no free-kick. I don't want to question his authority, but he was wrong.
Image source, ReutersGermany 2-0 Slovakia
Pat Nevin
Ex-Chelsea winger on BBC Radio 5 live
It does feel like Germany are conserving energy, coach Joachim Low is not happy with that, he has a few players warming up and needs to inject a bit of pace in the midfield.
Image source, EPAGermany 2-0 Slovakia
Julian Draxler clips Milan Skriniar and Slovakia have another opportunity from 30 yards out. Dead central.
Marek Hamsik rolls it to Juraj Kucka, but his shot initially looks like it's going wide and continues to spiral even wider. Not a great effort.
Germany 2-0 Slovakia
Germany have lost concentration momentarily. That crisp passing has gone a bit limp and Slovakia are seeing more of the ball.
Image source, ReutersGermany 2-0 Slovakia
And Hamsik curls it with his left foot, it brushes Mats Hummels in the wall as it spins over the bar. The referee misses the deflection and says goal kick.
Hamsik doesn't take kindly to the decision.
Image source, ReutersGermany 2-0 Slovakia
And they get reward for pushing up by winning a free-kick 30 yards out. Marek Hamsik is over it.
Germany 2-0 Slovakia
Pat Nevin
Ex-Chelsea winger on BBC Radio 5 live
Slovakia are trying to push further up the field, they were on their own 18-yard line for much of the first half.
The defence are pushing 20-30 yards further up to get in contact with their midfield, who in turn need to get in touch with the guys up front.
Image source, Getty ImagesGermany 2-0 Slovakia
Jan Kucka gets involved again - this time by stepping on Thomas Muller's foot. Looked a bit painful.
Germany 2-0 Slovakia
I was wondering what sort of impact Jan Gregus could make, considering he has number six on his shirt. But he immediately plays a slick throughball to Patrik Hrosovsky who gets to the by-line.
Marek Hamsik then tees up Juraj Kucka from 18 yards and he hits it into Manuel Neuer's arms.
Image source, EPAGermany 2-0 Slovakia
Joshua Kimmich is the first German in the book. He gets a yellow for handling the ball while trying to challenge Marek Hamsik.
Image source, Getty Images