Arsene Wenger's team bounced back from defeat against defending champion Manchester United with a dominant display, capped by two goals from Olivier Giroud — the first after Southampton goalkeeper Artur Boruc bizarrely lost the ball to the France striker in the box.
At Goodison Park, substitute Daniel Sturridge salvaged a deserved draw for the Reds before Chelsea reasserted its title credentials with a 3-0 win at West Ham.
Arsenal leads both Liverpool and Chelsea by four points after 12 games, with Liverpool in second place on goals scored.
Also, last-place Crystal Palace reacted to the hiring of Tony Pulis as manager by beating Hull 1-0 to climb off the bottom and Fulham lost 2-1 at home against Swansea, dropping into the bottom three. Newcastle beat Norwich 2-1 and Stoke won 2-0 against Sunderland, which replaced Crystal Palace at the foot of the standings.
"I'm very happy because we were against a good team and they showed why they made good results before," Wenger said after giving Southampton its second league loss this season. "We couldn't take our chances but we took advantage of their mistakes. It's a very good win against a difficult team. They stopped us well from playing."
Arsenal was sluggish at the start but then dominated before Boruc lost the ball after trying to dribble past Giroud, who easily won the ball before scoring from close range.
"It happens. Players are quick to close down. Maybe he was a bit too confident and Olivier Giroud did very well," Wenger said.
Southampton has been praised for its free-flowing football this season but struggled against Arsenal. The Saints played as high on the pitch and pressed as usual but failed to create clear-cut chances.
Frank Lampard made life difficult for his former club, scoring twice at Upton Park as Chelsea played with great pace and discipline to move above Southampton into third. Lampard opened the scoring from the penalty spot in the 21st minute after West Ham keeper Jussi Jaaskelainen brought down Oscar in the box. The Brazil midfielder then combined well with playmaker Eden Hazard and slotted home with a low shot from the edge of the box for a superb goal in the 34th.
Lampard sealed Chelsea's win, scoring from a rebound from inside the penalty area in the 82nd.
Liverpool had plenty of chances in a thrilling Merseyide derby which they came close to losing for the first time since October 2010.
But Sturridge equalized with a glancing header from Steven Gerrard's free kick just 10 minutes after coming off the bench to cap an action-packed game. The result left Liverpool four points behind Arsenal with 24 points from 12 games while Everton has 21, one point behind Southampton.
Romelu Lukaku scored twice in the second half as Everton took a 3-2 lead. The Belgian forward thought he had given the three points to his team when he headed home in the 82nd minute, just 10 minutes after taking advantage of some confusion in the Liverpool box to slide the ball past goalkeeper Simon Mignolet.
Philippe Coutinho opened the scoring in the fifth minute before Kevin Mirallas equalized for Everton three minutes later in a thrilling start. Luis Suarez put the Reds in front with a free kick in the 19th minute.
"That is the best experience I've ever had in club football. It's a pity we didn't win but hopefully we will next time," Lukaku said.
Mirallas was lucky to escape a straight red card in the 33rd minute after an ugly foul on Suarez, with the Belgium forward stamping his studs on the striker's thigh. Suarez screamed in pain and stayed down on the pitch for several minutes but was able to return to the game.
"It was a terrific game, I've been involved in a few and they are real heart-stoppers," Liverpool coach Brendan Rodgers said. "We again showed our resilience and ability to fight back. This is a difficult place to come and they haven't lost at Goodison Park this year."
Stoke ended an eight-match winless streak against Sunderland, which had Wes Brown sent off in controversial circumstances. The hosts scored either side of the interval at the Britannia stadium with goals from Charlie Adam and Steven Nzonzi.
Sunderland players were furious after referee Kevin Friend deemed a sliding tackle from Brown on Adam — that appeared to win the ball fairly for the defender — to merit a straight red card in the 36th minute.
Substitute Jonjo Shelvey scored a late winner to give Swansea a 2-1 victory over Fulham, leaving the London club struggling in the relegation zone.
At Hull, Palace overcame the 78th-minute sending-off of Yannick Bolasie to score the only goal three minutes later, with Barry Bannan netting from close range following Cameron Jerome's cross.
Caretaker manager Keith Millen hands over to Pulis with Palace now above Sunderland on goal difference, and the new coach's record of never having been relegated will give the Londoners renewed hope of staying up.