Lukaku put United ahead at the Hawthorns and Lingard netted with the aid of a deflection to double the visitors' lead before half-time.
Manchester City's thumping win over Tottenham Hotspur provisionally sent Pep Guardiola's men 14 points clear at the summit.
At Stamford Bridge, Chelsea sealed their second successive win to move within 11 points of City and draw level on points with second-placed Manchester United, who face West Bromwich Albion on Sunday.
Manchester City's win at Swansea made them the first team in the history of English league football to have won 15 games in a row.
Pep Guardiola's side, 2-1 winners at second-place Manchester United on Sunday, won comfortably at the Liberty Stadium to eclipse the mark of 14 successive wins set by Arsenal in 2002.
Tiemoue Bakayoko opened the scoring midway through the first half with a deft clipped finish, offering an answer to supporters who have criticised him for a series of poor performances following his July move from Monaco.
City's win at Old Trafford took them 11 points clear of United, their nearest challengers at the top of the table.
City are the first team to win 14 consecutive matches within the same season.
A single point, though, denied Arsenal the chance to climb into the top four.
Though Harry Kane scored twice, Son was the star of the show, scoring one goal and having a say in four others
Marko Arnautovic exchanged passes with Manuel Lanzini before wrong-footing Cesar Azpilicueta and placing the ball beyond Thibaut Courtois with his left foot.
Manchester United manager Jose Mourinho has launched a pre-derby attack on Manchester City's players by claiming it only takes a little bit of wind for them to go to ground.
Liverpool playmaker Philippe Coutinho has refused to commit his future to the Premier League club Liverpool.
City have drawn level with Chelsea in 2016-17 and Arsenal in 2001-02 for the most consecutive victories in a single season in Premier League history.
With Pep Guardiola's pacesetters not in action until Sunday, United's 3-1 victory took them to within five points of the Premier League summit following emphatic wins for Chelsea and Liverpool earlier in the day.
Liverpool are beginning to develop impressive momentum and have now collected 16 points from their last six league games.
Eden Hazard was in imperious form, scoring twice for Chelsea and running at defenders at will.
David Silva joined City from Valencia and has contributed to two Premier League title wins, two League Cup triumphs and one FA Cup success during his time at the Etihad Stadium.