Match ends, Belgium 3, Republic of Ireland 0.
Romelu Lukaku scored twice as Belgium recorded their first win at Euro 2016 and damaged the Republic of Ireland's chances of reaching the last 16.
After a goalless opening half, Lukaku scored the Belgians' first goal at the tournament with a neat finish from the edge of the area.
Axel Witsel headed in a second in the 61st minute, before Lukaku sidefooted home after a quick counter.
The Republic did not force goalkeeper Thibaut Courtois into a single save.
It means Martin O'Neill's side, who are bottom of their section with one point, will probably have to beat Italy in their final Group E game on Wednesday.
Belgium, meanwhile, are second on three points and next face Sweden.
It was a disappointing performance from the Republic after a promising display in their opening fixture, when they drew 1-1 with Sweden.
Shane Long, operating as a sole striker, found himself isolated for long periods but may feel he should have won a penalty when he was caught by a wild Toby Alderweireld boot inside the Belgium area, just before Lukaku opened the scoring.
Belgians back to their best?
Belgium boast a wealth of individual talent and had topped the Fifa rankings within the last year, making them one of the favourites to go far in France.
However, they looked nothing like a team capable of winning the tournament against Italy, against whom they lost 2-0 on Monday.
The Belgians lacked fluidity and a sense of unity. As goalkeeper Thibaut Courtois put it: Tactically, technically and organisationally, they came up short.
It was a different story against the Republic.
They dominated possession throughout, with Eden Hazard and Kevin de Bruyne proving much more effective at stretching their opponent's defence than they were against the Italians. Both finished with an assist each.
The win means they are in a strong position to finish second in the group and, while they will face opponents much more attack-minded than the Republic, the victory will undoubtedly boost a side that had appeared lacking in confidence at the start of the tournament.
Play it long to Long
Before Saturday's game, Belgium's De Bruyne had suggested the Republic would be one of their toughest opponents because of their physical power.
An element of that physicality was missing on Saturday with Jon Walters not deemed fit enough to take his place in the side, but the Republic had showed against Sweden on Monday that they have another side to their game.
With the impressive Wes Hoolahan pulling the strings in midfield that day, the Republic were composed on the ball, retaining possession to build attacks before deservedly taking the lead.
Time on the ball was not as forthcoming against Belgium and when they did have possession, they went long. However, without Walters' ability to hold up the ball, it was a tactic that did not work.
Lukaku's opener did force the Republic to abandon their cautious approach but that in turn left gaps at the back for their increasingly confident opponents to exploit, which they did to full effect.
"Overall it was very, very poor," said BBC Radio 5 live co-commentator Kevin Kilbane, won won 110 Republic of Ireland caps.
"Creativity was slack and there was no real spark in the side. I'm looking for a lot more going into the Italy match."
Lukaku makes up for poor Italy display
With no goals in 11 competitive games for club and country, Lukaku's place in the Belgium starting XI had come under scrutiny, especially after a lacklustre display against Italy.
In the first half against the Republic, he struggled to make an impact once again. The Everton striker did not have a single shot on goal in the opening 45 minutes, nor did he complete any successful dribbles or create a chance.
Coach Marc Wilmots resisted the temptation to replace him at half-time with Divock Origi, and it was a decision that paid off.
Moments after the second half started, Belgium hit their opponents on the break as De Bruyne fed Lukaku on the edge of the area and he placed the ball beautifully into the corner of the goal. He then showed good composure to pass the ball into the net following excellent work by Hazard for his second and Belgium's third.
If Belgium are to go far in this tournament, they will need Lukaku to perform like he did in the second half of this game on a consistent basis.
Man of the match - Romelu Lukaku
What they said
Republic of Ireland boss Martin O'Neill: "You have to analyse the performance and assess where mistakes are made. The first goal was vitally important and that came from our attack - they broke and got the goal. Then as we started to chase the game we got caught a few times, Belgium are a good side and put the game beyond us.
"We're bit disappointed with our performance considering how well we played against Sweden. We have to win this game against Italy and we feel that, once we've freshened ourselves up again, we'll be ready to go."
Belgium coach Marc Wilmots: "Unity is very important. We win and lose together.
"With Romelu Lukaku, we wanted to give him some confidence. I think he scored four goals in four matches but when he missed against Italy everyone was saying it's all different. I just needed to explain things to him and make sure he knew I trusted him. He did what I expected today."
The stats you need to know
- Republic of Ireland are still winless at the Euros since beating England in their first game in the competition in 1988 (D2 L5).
- Kevin de Bruyne has had a hand in 10 goals in his past 10 appearances for Belgium (five goals, five assists).
- Lukaku became the sixth Belgian to score at both the World Cup and the Euros.
- The striker is also the first Belgian to score twice in a major tournament match since Marc Wilmots did so against Mexico in the 1998 World Cup.
- The Republic of Ireland have kept just one clean sheet in eight competitive matches against Belgium.
- Axel Witsel's goal was his first for Belgium since September 2014 (against Australia), 653 days ago.
- There were 28 passes in the build up to Witsel's goal, a record for the European Championships (since 1980).
- Republic of Ireland failed to have a shot on target in a major tournament game for the first time since the 1994 World Cup (against Norway).
- This equalled Belgium's biggest win at a major tournament (equalling their 3-0 victory over El Salvador at the 1970 World Cup).
The Republic of Ireland face Italy at the Stade Pierre-Mauroy in Lille in their final group game on Wednesday. Belgium's victory means the Italians have won the group, but Wilmots' side are favourites to finish second. A win against Sweden in Nice on Wednesday will ensure they do.
- 3VermaelenBooked at 49mins
- 19DembéléSubstituted forNainggolanat 57'minutes
- 11CarrascoSubstituted forMertensat 64'minutes
- 7De Bruyne
- 10E Hazard
- 9LukakuSubstituted forBentekeat 82'minutes
- 21J Lukaku
R. of Ireland
- 13HendrickBooked at 42mins
- 8McCarthySubstituted forMcCleanat 62'minutes
- 20HoolahanSubstituted forMcGeadyat 71'minutes
- 9LongSubstituted forKeaneat 79'minutes
- Cüneyt Çakir
- Shots on Target
Second Half ends, Belgium 3, Republic of Ireland 0.
Attempt missed. Aiden McGeady (Republic of Ireland) header from the centre of the box misses to the left. Assisted by Robbie Brady with a cross.
Eden Hazard (Belgium) wins a free kick in the defensive half.
Foul by Seamus Coleman (Republic of Ireland).
Attempt blocked. Jeff Hendrick (Republic of Ireland) right footed shot from outside the box is blocked. Assisted by Robbie Keane.
Attempt missed. Stephen Ward (Republic of Ireland) left footed shot from outside the box is too high. Assisted by Seamus Coleman with a cross.
Attempt missed. James McClean (Republic of Ireland) left footed shot from outside the box is close, but misses to the right from a direct free kick.
Foul by Radja Nainggolan (Belgium).
Robbie Keane (Republic of Ireland) wins a free kick in the attacking half.
Attempt saved. Kevin De Bruyne (Belgium) left footed shot from outside the box is saved in the centre of the goal. Assisted by Axel Witsel.
Substitution, Belgium. Christian Benteke replaces Romelu Lukaku.
Attempt blocked. Robbie Brady (Republic of Ireland) left footed shot from outside the box is blocked. Assisted by Jeff Hendrick.
Attempt missed. Dries Mertens (Belgium) right footed shot from outside the box is close, but misses the top right corner.
Attempt missed. James McClean (Republic of Ireland) header from the centre of the box is close, but misses to the right. Assisted by Robbie Keane.
Substitution, Republic of Ireland. Robbie Keane replaces Shane Long.
Corner, Republic of Ireland. Conceded by Jan Vertonghen.
Attempt missed. Dries Mertens (Belgium) right footed shot from outside the box is close, but misses to the left. Assisted by Romelu Lukaku.
Substitution, Republic of Ireland. Aiden McGeady replaces Wes Hoolahan.
Goal! Belgium 3, Republic of Ireland 0. Romelu Lukaku (Belgium) left footed shot from the centre of the box to the bottom left corner. Assisted by Eden Hazard following a fast break.