Slovakia had defeated the Germans 3-1 in a pre-tournament warm-up game last month but there was to be no repeat on Sunday as Boateng drilled in the opener after eight minutes and Mario Gomez flicked in a second goal, after Mesut Ozil had seen a penalty saved, just before half-time.

Julian Draxler put the result beyond doubt just after the hour mark and Germany, seeking an unprecedented fourth European Championship title, will play the winner of Monday's clash between Italy and Spain in the last eight in Bordeaux on Saturday.

The Stade Pierre Mauroy held good memories for both teams with both winning at the stadium in the group stages, with Germany beating Ukraine and Slovakia winning against Russia, but it was the world champions who adjusted quickest to the newly-laid pitch.

A lively start by Joachim Low's side was soon rewarded. Toni Kroos' corner was headed out by Milan Skriniar but only as far as the edge of the penalty area where Boateng returned the ball with a low shot which flicked off Skriniar en route to the bottom corner of the net.

Germany had the chance to extend their lead after 13 minutes when Martin Skrtel pushed Gomez in the back but Matus Kozacik dived to his left to push away Ozil's penalty kick.

Germany were a constant threat and it seemed only a matter of time before they would score again. Kroos and Ozil sent efforts narrowly wide and Thomas Muller brought a smothering save from Kozacik before the half hour mark.

Draxler then showed good strength and technique to control the ball on the edge of the penalty area before turning and shooting just wide in the 39th minute.

The second goal finally came two minutes before half-time and Draxler was the architect, brilliantly drifting past Juraj Kucka and getting to the byline inside the box where he picked out Gomez at the near post who flicked the ball in from close range.

Draxler got on the scoresheet himself in the 62nd minute when he was afforded too much time and space inside the six-yard box to spin and volley home a loose ball following a corner. It was a shame for Slovakia who had started the second half well but now faced an almighty task to get back into the match, which never seemed likely.

Jan Durica tried to reduce the deficit as the midway point of the second half approached and his driven low free-kick worried Manuel Neuer enough for the German goalkeeper to fling himself across his net, but the ball flew wide.

Confident progression was assured so Low made changes, taking off scorers Boateng and Draxler as well as Sami Khedira.

Germany still created opportunities, the best of which saw Muller cut the ball back for Kroos but Kozacik parried away his effort in injury-time.