France, Germany and Belgium sealed their places in the quarterfinals of the European Championship on Sunday as three of the pre-tournament favorites lived up to their promise.

There was a scare for the host nation after Ireland scored a second minute penalty, but Antoine Griezmann struck twice after the break to give France a deserved 2-1 victory in Lyon.

While France was made to work hard to advance, Germany had no such difficulties in a polished 3-0 victory over Slovakia, whileEden Hazard inspired Belgium to what ended up as a crushing 4-0 win over Hungary.

The goals and the quality of the football over the three games were a marked improvement on the dire performances witnessed on Saturday when Poland, Wales and Portugal advanced.

The relief was palpable at the Stade de Lyon after France finally overwhelmed an Ireland side that had led through Robbie Brady’s spot-kick, after France midfielder Paul Pogba bundled Shane Long to the ground.

Ireland chased for every ball and worked tirelessly to defend its slender lead. But Griezmann’s two goals in the space of three minutes midway through the second half saw the natural order restored, and a red card for Shane Duffy in the 66th minute all but ended the contest.

”When Ireland took the lead it made us a bit more uncomfortable in the first half,” France coach Didier Deschamps acknowledged. ”They showed a lot of enthusiasm, but we had to dig deep, get through the situation and get in front.”

France’s reward is a quarterfinal next Sunday at the Stade de France in Saint-Denis against either England or Iceland, which play in Monday’s late kickoff.

Germany scored early and never looked back against a Slovakia side that had surprisingly beaten Joachim Loew’s world champions in a friendly last month.

Jerome Boateng broke the deadlock after just eight minutes in Lille with a deflected shot, his first goal in 63 appearances for Germany.

Mesut Ozil missed a penalty shortly afterward, the first by a German player at a European Championship since 1976. ButMario Gomez stabbed home Germany’s second just before the break after a clever cutback by Julian Draxler, who then volleyed home the third midway through the second half.

”Now the games that we’re looking forward to are coming,” Gomez said. ”They’re why we came to the European Championship. Of course we want the title. And for that you have to beat such teams.”

If Slovakia proved to be a relatively easy proposition, the same cannot be said of Germany’s next opponent – either two-time defending champion Spain or Italy, which meet on Monday. That quarterfinal will be played on Saturday in Bordeaux.

Hazard may be coming off a very mediocre season with Chelsea, but he lit up the Stade de Toulouse on Sunday.

After Toby Alderweireld headed Belgium into a 10th minute lead, Hazard turned victory into a rout in the closing stages.

He began by surging past Hungary’s defense on the left side and sending over a low cross for substitute Michy Batshuayi to steer home in the 78th minute – just two minutes after coming on.

The Chelsea playmaker then followed up by scoring a spectacular solo goal, breaking down the left on a counterattack before cutting inside, skipping past three Hungary defenders and curling a shot into the bottom right corner.

Substitute Yannick Ferreira Carrasco struck the fourth in added time as Belgium lined up a quarterfinal against Wales on Friday in Lille.

”We should have been 3-0 up after the first half,” Belgium coach Marc Wilmots lamented. ”We kept the game 1-0 too long. We needed too many chances, and in big games we usually don’t have so many chances.”

There could be no such complaints about Hazard.

Asked if it was his best performance for Belgium, Hazard simply said ”Yes”, before breaking into a smile.

Written by Trevor Huggins of the Associated Press