LILLE, June 27 — Jerome Boateng volleyed his first goal for Germany and Belgium's Eden Hazard was on target for the first time at Euro 2016 as their sides powered past Slovakia and Hungary to claim quarter-final places.
They joined tournament hosts France who needed an Antoine Griezmann double to inspire a fightback from a goal down against the Republic of Ireland to win 2-1.
World Cup holders Germany never looked troubled by a Slovakia side which had beaten them 3-1 in a recent friendly and held England to a goalless draw. But even with a 3-0 win, coach Joachim Loew said Germany will have to deliver more to hope to lift the European Championship trophy.
Boateng's 25-metre power drive after eight minutes at Lille was the Bayern Munich centre-back's first goal for his country. “I hit the ball well and am glad it went in. It was also about time,” said Boateng.
Mesut Ozil had a penalty saved soon after but Julian Draxler set up Mario Gomez to double the lead two minutes before half-time and the impressive Draxler then completed the scoring just after the hour mark.
“We put in a great effort, both defensively and going forward, but with all due respect to our opponents we cannot say from this that we are going to dominate the competition,” said Loew.
“We will have to improve to win the tournament.”
Hazard proved a constant threat as Belgium hit four goals past Hungary, one of the surprise packages of Euro 2016.
Belgium were dominant from start to finish in Toulouse.
Toby Alderweireld headed them into a 10th-minute lead and the Red Devils wasted a series of great chances before Michy Batshuayi with his first touch as a substitute, Hazard and Yannick Carrasco scored in the last 12 minutes.
Belgium will play Gareth Bale's Wales in the quarter-finals.
France coach Didier Deschamps read the riot act to his side at half-time to inspire the Griezmann-led revival against the Irish Republic who went ahead inside two minutes through a Robbie Brady penalty.
Goal hero Griezmann said the dressing-room exchanges had been "stormy" but did the trick along with a tactical switch which saw him brought more into the centre of the field to tear into the Irish defence.
The Atletico Madrid striker headed the equaliser and four minutes later drove in a second goal to propel his team into a last-eight meeting with England or Iceland.
“I can raise my voice at half-time,” said Deschamps.
“I am not going to tell you what was said. We needed to be calm and not get annoyed. The players spoke, and not just those who were on the field.”
“We put our heart and soul into the game,” said Ireland coach Martin O'Neill, who had complained before the game that not enough tickets had been allocated to Irish fans.
“Maybe if we had gone a few more minutes without conceding, France might have got a bit panicky, but then they scored in quick succession.”
Today sees the last 16 games completed with Italy taking on Spain in a repeat of the Euro 2012 final — which Spain won 4-0 — and England playing Nordic underdogs Iceland in Nice.
Some 25,000 England fans and 10,000 from Iceland were expected in the Mediterranean city where the stadium has a 35,000 capacity. — AFP