Manchester City took the lead in the 17th minute with Aguero continuing his remarkable run of goalscoring form at the Etihad.
Lukaku's first-half double was enough for a well-earned three points as United bounced back from consecutive defeats to Brighton and Tottenham.
The 31-year-old, who failed to make the England squad for the World Cup, has signed a two-year contract.
West Ham United captain Mark Noble pinned one fan down to the ground and his team-mate James Collins asked the remaining two fans to leave.
The Clarets thought they had rescued a point when they equalised on the 87th minute, but Ragnar Klavan met Dejan Lovren's header in the final moments.
Manchester United came from two goals down to rescue a dramatic 2-2 draw against Burnley thanks to Jesse Lingard's double.
Harry Kane took his goal tally in the Premier League to 36 for the calendar year, equalling the record set by Alan Shearer with Blackburn Rovers in 1995.
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.
Sergio Aguero's hat-trick inspired a 6-0 demolition of Watford.
Arsenal's defeat, and the toothless manner of their surrender, will once again raise questions about Wenger's position, less than three months after the Frenchman signed a new two-year contract.
Sam Vokes scored twice as Burnley torpedoed defending champions Chelsea 3-2 at Stamford Bridge on Saturday in one of the most sensational opening-weekend results in English top flight history.
Liverpool defeated Burnley 2-1 with Georginio Wijnaldum and Emre Can scoring winning goals in the Premier League.
While Millwall upset defending Premier League champions Leicester City 1-0, Lincoln City stunned top flight club Burnley 1-0 in the fifth round of FA Cup on Saturday.
While Chelsea drew 1-1 against Burnley, Premier League defending champions Leicester City lost 0-2 to Swansea City on Sunday.
Arsenal were 1-0 up courtesy of Shkodran Mustafi's first goal for the club when, in the third of seven minutes of time added on by referee Jon Moss, Burnley's Ashley Barnes was fouled inside the area by Francis Coquelin.
While Liverpool stumbled and Manchester City strolled, champions Leicester City are still awaiting the first win of their title defence after being held to a goalless draw by Arsenal
Alexis Sanchez scored the winner for Arsenal as the defending champions cruised to a 2-1 win over second-tier side Burnley in FA Cup.
Bottom placed Burney and QPR slid further towards relegation following their loses to West Ham and Liverpool, respectively. Burnley lost 1-0 at West Ham United while Liverpool cruised to a 2-1 win over QPR.