There are far bigger tests to come for Belgium, starting with England in Kaliningrad on Thursday, but Roberto Martínez’s players have signalled their intent, racking up maximum points from their opening two matches, scoring freely and looking like a team who plan to live up to their billing as one of the leading contenders for the World Cup.

Belgium scored five but it is no exaggeration to say the goal count could easily have ended up in double figures on a day when Romelu Lukaku and Eden Hazard grabbed two apiece and Michy Batshuayi, on as a substitute for the Chelsea playmaker, contrived to miss a hat-trick of simple chances before he finally converted. Cue the loudest cheer of the afternoon.

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For Lukaku, who ended the game as the tournament’s joint‑leading scorer with Cristiano Ronaldo, it was a landmark day. At the age of 25 Lukaku has more goals in major tournaments than any other Belgian and he also became the first player to score two or more in successive World Cup games since Diego Maradona in 1986. Presumably this is what Lukaku had in mind when he said on the eve of the tournament: “I’m going to remember to have fun this time.”

Belgium look a team who are having fun full stop. With their slick passing and fluid movement, they are a joy to watch going forward. Lukaku, who is blessed with so much creativity around him, would surely have ended up with a hat-trick had he not been withdrawn with half an hour remaining, after Martínez decided to take no chances with an ankle injury that the Manchester United striker picked up just before the interval.

Belgium were 4-1 up by the time Lukaku departed, playing with a swagger and, inspired by the mercurial Hazard, threatening to open up Tunisia every time they ventured into their opponents’ half. Hazard, on this evidence, is determined to show a wider audience why he deserves to be recognised among the most distinguished players in world football. His spot-kick in the fifth minute opened the scoring and there was a touch of class about the way he took his second, expertly sidestepping Farouk Ben Mustapha, the Tunisia goalkeeper, before slotting home. The statistics – 10 goals and 12 assists in his past 20 appearances for Belgium – highlight just how influential Hazard has become to this side.

There is, however, quite a supporting cast behind him and Lukaku. Dries Mertens, who scored a splendid goal in the opening game against Panama, set up Lukaku’s first. Thomas Meunier was a rampaging presence on the right, and then there is Kevin De Bruyne, who makes everything tick at the base of the Belgium midfield alongside Axel Witsel.

Facebook Twitter Pinterest Romelu Lukaku clips his second goal past Farouk Ben Mustapha of Tunisia to join Cristiano Ronaldo at the top of the goalscoring charts. Photograph: Abedin Taherkenareh/EPA

It is a measure of just how free-flowing Belgium were here that Batshuayi, who came on for Hazard, had so many chances during his 22 minutes on the pitch. Youri Tielemans, another substitute, delivered the cross that Batshuayi eventually converted, after seeing one shot cleared off the line, another come back off the bar and Ben Mustapha deny him with a point-blank save.

Belgium, in other words, were rampant and it would be fair to say Tunisia gave them a helping hand with some dreadful defending. To their credit Tunisia never gave up and they will take some comfort – as may England – from the fact that they managed to score twice against Belgium. Dylan Bronn got the first, before leaving the pitch in tears six minutes later with what appeared to be a serious knee injury, and Wahbi Khazri, impressive throughout, scored the second in injury time.

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Although Belgium are mathematically not through to the last 16, it would take a bizarre and almost unthinkable set of results for Martínez and his players to miss out on a place in the next phase. Tunisia will be eliminated if Gareth Southgate’s side avoid defeat by Panama on Sunday.

The expectation was that Tunisia would try to frustrate Belgium in the same way they did England for long periods but that gameplan went out the window inside six minutes. Syam Ben Youssef made a reckless challenge on Hazard that prompted Jair Marrufo, the referee, to point to the spot. After a slight delay while the video assistant referee checked whether contact was made inside the area, Hazard calmly rolled in his penalty.

In the blink of an eye it was 2-0. Mertens, capitalising on a heavy first touch by Ali Maâloul, the Tunisia left‑back, carried the ball forward before releasing Lukaku, who steadied himself before shooting low across Ben Mustapha. What followed was not in the script as Tunisia pulled a goal back within two minutes. Khazri delivered an inswinging free-kick that Bronn, who plays his football in Belgium for Gent, headed past Thibaut Courtois.

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Lukaku then restored Belgium’s two-goal advantage on the stroke of half-time with a lovely finish from Meunier’s terrific pass. Ben Mustapha had dashed from his line, trying to narrow the angle, but Lukaku deftly lifted the ball over him. Belgium did not have to wait long for their fourth, which owed much to the vision of Toby Alderweireld, who picked out Hazard’s intelligent run in behind the square Tunisia defence.

Then came that flurry of missed chances for Batshuayi, prompting gasps of amazement in the stands, before finally he made it 5-1. Even then Tunisia kept trying to attack, and their admirable perseverance was rewarded when Khazri, who spent last season on loan at Rennes from Sunderland, completed the scoring with a first-time shot.