Midfield anchorman Nemanja Matic bossed the centre of the pitch, allowing a rejuvenated Paul Pogba to venture forward and score his second goal in two games, while striker Romelu Lukaku netted his third, after selfless work throughout the match.
Henrik Mkhitaryan and substitute Anthony Martial, who again scored as a late substitute, also continued to thrive.
A 10-man West Ham conceded a stoppage-time penalty, after fighting back from 2-0 down at Southampton to lose 3-2.
Javier Hernandez's double either side of halftime had seemed to complete an astonishing comeback for West Ham, which trailed after Manolo Gabbiadini and a Dusan Tadic penalty put the Saints two up with their first home league goals since April.
In between, West Ham striker Marko Arnautovic received a straight red for elbowing Jack Stephens in the face, his second dismissal against Southampton in two seasons.
But West Ham refused to buckle and Mexican Hernandez thought he had done enough to earn a point, before Pablo Zabaleta bundled over Maya Yoshida deep into added time and Austin converted the spot-kick.
Watford and West Brom had away wins over Bournemouth and Burnley respectively, while at Anfield, Sadio Mane struck in the 73rd minute for Liverpool to scrape past Crystal Palace.
Socceroos gloveman Mat Ryan's tough start to life in the Premier League has continued, after Shinji Okazaki struck early and Harry Maguire netted a header from a corner, as Leicester City beat Brighton 2-0 at home.
Japanese international Okazaki was on hand to rifle home the rebound from a Riyad Mahrez shot in the first minute, as the 2016 Premier League champions got off to a flying start in their first home game of the season.
Mahrez was also behind Leicester's second goal, swinging a corner early in the second half, for Maguire to head home his first goal for the Foxes.
