Arsene Wenger had seen his side beaten by Borussia Dortmund and Chelsea in their previous two home games, but they prevailed through goals from Santi Cazorla and Aaron Ramsey to confirm their role as the team to beat.
Liverpool arrived at the Emirates Stadium hoping to leapfrog Arsenal to the top of the table, but the hosts took a 19th-minute lead when Cazorla hooked home after an initial header came back off the post.
The irrepressible Ramsey added a second just before the hour with a glorious strike, lifting a half-volley into the top-left corner from 25 yards to take his tally of goals to 10 in all competitions.
Luis Suarez spurned two late chances for the visitors, but Arsenal emerged unscathed as they increased their advantage over second-place Chelsea and third-place Liverpool to five points.
"It was a convincing win against a good team and that's what we wanted," said Arsenal manager Wenger.
The display was particularly encouraging in the light of comfortable wins for Manchester United and Manchester United earlier in the day, but Wenger played down the significance of his side's early lead.
"It's positive and nice, but of course it's very early in the season," he told Sky Sports.
"It's good for the confidence of the team and the ambition as well, and hopefully it gets everybody around the team to support us and continue to do that."
United maintained their recent momentum by winning 3-1 over Fulham at Craven Cottage to record a fourth consecutive victory in all competitions.
David Moyes's side effectively wrapped up the game inside 22 minutes through goals from Antonio Valencia, Robin van Persie and Wayne Rooney.
Alex Kacaniklic pulled a goal back for Fulham in the 65th minute with a shot that deflected in off Rooney, but the champions saw out a victory that elevated them to within two points of the top four.
"It's always been my team since I've taken over from Sir Alex Ferguson," said United manager Moyes.
"It can take time to settle in and it has for us, but Manchester United usually make slow starts and get better as the season goes on."
City moved into the Champions League places after bouncing back from a 2-1 loss at Chelsea last weekend by demolishing Norwich City 7-0 at the Etihad Stadium.
City manager Manuel Pellegrini created a stir by dropping goalkeeper Joe Hart following a succession of blunders, but he saw his side race into a 4-0 lead through a Bradley Johnson own goal and efforts from David Silva, Matija Nastasic and Alvaro Negredo.
Yaya Toure added a fifth with a sumptuous free-kick on the hour before Sergio Aguero bludgeoned home in the 71st minute and substitute Edin Dzeko added a late seventh.
"We were very unhappy when we lost against Chelsea, but we didn't deserve to lose that match," said Pellegrini, whose side trail Arsenal by six points.
"So we continued playing the same way. Norwich did not have a chance to score, we scored seven and could have scored more."
Chelsea could only watch as their rivals ran riot after falling to an unexpected 2-0 loss at Newcastle United in the day's early-off kick.
Chelsea captain John Terry hit the bar and had a header cleared off the line in the first half, but Newcastle prevailed through Yoan Gouffran's 68th-minute diving header and a late Loic Remy strike.
"I didn't like it. I think we deserved to lose," Chelsea manager Jose Mourinho told BT Sport.
"We had a couple of good chances to score the equaliser, but they were in the game more than us, they fought more than us and they were much more committed than us."
The day also witnessed a freak goal by Stoke City goalkeeper Asmir Begovic, who scored the quickest goal of the season to date with a wind-assisted 98-yard clearance that bounced over Southampton counterpart Artur Boruc after only 13 seconds.
However, Jay Rodriguez's 42nd-minute header from a raking James Ward-Prowse cross earned visitors Southampton a 1-1 draw that kept Mauricio Pochettino's side in the top five.
Hull City manager Steve Bruce enjoyed a 1-0 home win over former club Sunderland. Carlos Cuellar's first-half own goal decided the game and Sunderland had both Lee Cattermole and Andrea Dossena sent off before half-time for ugly fouls.
Efforts from Saido Berahino and Gareth McAuley gave West Bromwich Albion a 2-0 win at home to bottom club Crystal Palace, while West Ham United and Aston Villa drew 0-0 at Upton Park.