Penalty shootouts often tend to boil down in the memory to a single tear-stained snapshot. At the end of Brazil and Chile’s World Cup last-16 shootout in Belo Horizonte last weekend it was Júlio César’s sobbing post-match interview, replayed relentlessly on Brazilian TV, that seemed to capture the sense of overwrought fraternal catharsis, and also to point most clearly to the sheer scale of the collective emotional breakdown narrowly averted by Júlio César’s saves and a helpful goalpost.

There are two points that perhaps got a little lost in all this. First, and by way of a tangent, imagine for a moment what this most bizarrely emotional and highly-strung Brazil squad are going to be like when and if they actually lose at this World Cup.

And second, for all Júlio César’s saves it was actually David Luiz, current No1 ranked player at this World Cup, according to Fifa, who provided the most visible source of inspiration in those vital moments. Just as it is David Luiz ahead of Friday’s fraught-looking quarter-final against Colombia in Fortaleza who provides not just a very clear sense of leadership on and off the pitch but also – and yes this is the same David Luiz – a rare sense of calm.

It might not have been obvious from the television pictures but David Luiz was all over that shootout. Not only did he put Brazil’s first penalty away in his usual emphatic fashion, he also led the theatre, walking halfway to the area to congratulate each successful taker – Brazilian or Chilean – performing a near half-lap of the pitch when Brazil went ahead and generally giving the impression the entire spectacle was taking place in his back garden.

As in a sense it kind of was. Make no mistake: David Luiz is an absolute star in Brazil, not just as a player, where the Premier League notion of his flakiness never crossed the Atlantic, but as a Seleção statesmen off the pitch: voice of reason, respected leader and a genuine blue-chip celebrity in this football-centred nation of 199 million people.

It is David Luiz’s face that peers out from the adverts, including one for an airline that features him in pilot pose, grinning zanily in front of a waiting jet (how reassuring is this really?) and David Luiz along with Neymar whose name is on the replica shirts being hawked by Fortaleza street vendors. He talks brilliantly well on camera. His impassioned singing of the national anthem has become a pre-match staple for Brazil’s fans. Give it a few years and it’s not too hard to imagine him ending up as defence minister or governor of Sao Pãulo state.

For now, though, he has simply been vital to Brazil’s progress, playing consistently well in a team that is set up nicely to accommodate his style of play. David Luiz’s main attributes – that supreme athleticism and confidence on the ball – have been well complemented by Thiago Silva’s positional intelligence and tackling ability, not to mention the presence in front of both of a pair of gristly midfield pivots.

More broadly David Luiz’s mobility is a crucial factor in what is a notably restrained Brazil. There are basically two free(ish) players in Luiz Felipe Scolari’s team: Neymar up front and David Luiz coming out from the back. Together they do what they can to break up the lines in a team that resembles at times the football equivalent of a musclebound nightclub bouncer unable to do much more than tap his foot and raise an eyebrow when the music comes on.

It is a part of David Luiz’s role that will come into shaper focus against Colombia. Luiz Gustavo has been Scolari’s most dependable defensive midfielder. His absence through suspension means David Luiz might have to develop a taste for lateral as well as forward movement, covering his own full-backs a bit in the classic British style.

At the same time what David Luiz has done so well at this World Cup, those sprints out of defence to intercept or smother danger between the lines, will surely be key to Brazil’s attempts to stifle James Rodríguez. Colombia’s star man has been incisive when cutting inside and exploiting space 40 yards or so from goal.

David Luiz will, being David Luiz, find himself coming out at times to meet him. There will be lunges, blocks, interceptions. How well the world’s most expensive defender does all this will surely be a key element in how the game plays out. But then David Luiz has been key to Brazil under Scolari 2.0 from the start, a player who never really looked like a Premier League centre back – where absolute defensive concentration is prized above mobility or ball-playing skills – but who has been key to the construction on the hoof of Brazil’s current World Cup team. To date 23 of his 40 caps have come in Scolari’s 26 games in charge, while Brazil under Scolari have never lost when David Luiz has played the whole match.

And beyond the team itself Paris Saint-Germain’s star summer purchase remains not just a billboard celebrity but an important figure generally in Brazil’s ability to embrace fully its own Seleção.

The relationship between team and public has taken a few hits in recent years. The Nike years, when Brazil would play friendlies any time anywhere (except Brazil) hardly helped, although no doubt that Andorran fan-base lured in by playing there just before the 1998 World Cup is still hungrily buying shirts. Plus, of course, so many of Brazil’s players have disappeared overseas in the first bloom of their talent.

David Luiz played 26 matches for Salvador’s Vitória seven years ago before he was sold to Benfica and made his debut for Brazil in 2010 having played almost entirely abroad as a professional. And yet, with his charm and São Paulo sang-froid, he has played a major part in bridging this temporary divide, a leader of the diaspora players, and a major component in the emotional heart of this united, impassioned, at times rather fraught, Brazilian team.