Luiz produced another virtuoso display yesterday to help the champions edge past Manchester City 2-0 and maintain their late charge in defence of the title.
Chelsea went into the international break nine points behind faltering leaders United with a game in hand, having also drawn them in the quarter-finals of the Champions League.
Gunning for the top: David Luiz believes Chelsea can catch Man United
Luiz, who is cup-tied for the latter clashes at the beginning of next month, has backed his team-mates to end United's European dream, while vowing to help the Blues complete what would be one of the most incredible title comebacks in Premier League history.
'We want to do everything this season,' said Luiz.
'We want to catch United in the Premier League and beat them in the Champions League. We have to believe - we can win the title.
'There are still many games and a lot of points to play for.
'I can't play in the Champions League because I am cup-tied but I am very close to the team.
'The happiness of my team-mates will be my happiness if they do well.'
Revelation: Defender Luiz has scored twice already since joining from Benfica
The ?25million signing of Luiz has co-incided with Chelsea's Premier League revival, with the champions having trailed United by 15 points at one stage.
The former Benfica centre-back has been a revelation, demonstrating the full range of his defensive and attacking skills and making himself an instant hero with his new side's supporters.
Indeed, the 23-year-old Brazil star has now scored crucial goals against United and City in his two starts at Stamford Bridge.
He said, modestly: 'I am really delighted that the fans have taken to me so soon but the best thing is that the team are in good shape.
'I always work hard and like to help the team.
'Of course, when the team are doing well it is much easier.
'It has become easy for me to settle in because the players and the manager have helped me.'
Gauntlet: Carlo Ancelotti has challenged his players to win all their remaining games
New arrivals at Chelsea go through an initiation, which involves them singing a song to their team-mates.
Luiz refused to reveal what he sang, saying: 'It is our secret. But I have sung the song and it was okay.'
Manager Carlo Ancelotti yesterday challenged his players to keep the pressure on United by winning all of their remaining games.
And City defender Vincent Kompany urged his own side to take maximum points from their last eight league matches to ensure they do not throw away a Champions League spot for the second successive season.
Yesterday's defeat killed off any faint hope Roberto Mancini's men had of launching their own comeback in the title race.
It also left them in real danger of being beaten by Tottenham in the battle for fourth place, just as they were last year.
Belgium defender Kompany is all too aware there is a sense of deja vu, with Spurs once again set to travel to the City of Manchester Stadium late in the season.
Keeping the faith: Vincent Kompany is refusing to give up on Man City's title hopes
'We are around third and fourth, so definitely want to make sure we can stay there and see afterwards what happens,' Kompany said.
'We look at the schedule and think we have a good chance.
'My target is to win every game that is left. The teams around us are not guaranteed to get all the points so there is still something to do.'
City's mega-rich owners are unlikely to tolerate a second failure by Mancini, who may also have been expected to put up more of a title challenge.
But Kompany said: 'It was never going to be straightforward to say we want to be champions and then become champions.
'The important thing is that we are improving and no-one can hold it against us if we do that.
'If we do that and then improve again next season, we have done our job, and then one day we will be up there.'
Salomon Kalou insists it does not matter that he and Chelsea's other strikers have all flopped in front of goal since Fernando Torres arrived at the club.
Kalou is adamant his only concern is that the Blues are winning and keeping alive their hopes of a sensational comeback in the Barclays Premier League title race.
Kalou, Torres, Didier Drogba and Nicolas Anelka have all failed to find the net in the league since ?50million man Torres made his debut against former club Liverpool six weeks ago, and Drogba and Torres have only managed one shot on target between them since the Spaniard joined.
Not concerned: Salomon Kalou believes Chelsea's strikers are contributing enough to their game
But Chelsea's midfielders and defenders have stepped up in recent weeks in front of goal to help put together a hat-trick of wins to stay in touch with Manchester United at the top of the table.
Kalou, who started yesterday's 2-0 victory over Manchester City, told the club's official website, www.chelseafc.com: 'It doesn't matter who scores because, when you are coming back to the top as a team, you have to focus more on the result.
'There are some moments when it's the defenders who score and the most important thing is that the team must stick together and win games.'
Chelsea's victory yesterday lifted them above City into third place, nine points behind United with a game in hand.
Kalou added: 'That's one of our best games, where we've put the team under pressure and where we keep the ball and create chances.
'That's our level, so I believe if we continue like that, we can put Man U under pressure.
'It was very important for us to win and now we've got to the third place and we are coming back to our best.
'You can only take it game by game and we have to focus on our own game.'
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