Arsenal has taken 25 points out of 30 possible this season and are five points clear of Chelsea and Liverpool.
Also, Manchester City crushed Norwich 7-0 to maintain its perfect home record, and Manchester United beat Fulham 3-1, scoring three times in the space of 13 minutes courtesy of goals from Antonio Valencia, Robin van Persie and Wayne Rooney.
In a game involving two of the most exciting teams this season, Arsenal easily came out on top with a display of authority and resilience.
Cazorla broke the deadlock for the Gunners with a volley in the 19th minute, scoring from the rebound after his header hit the post. Aaron Ramsey then beat Liverpool keeper Simon Mignolet with a bolt from 20 yards in the 59th.
"It was a convincing win against a good team which is what we wanted. We responded well to losing in midweek." Arsenal manager Arsene Wenger said, referring to a 2-0 loss against Chelsea in the League Cup.
"The first goal was a vital moment. After that I felt we had the opportunities to make a difference and Aaron Ramsey scored a stunning goal. Five points clear is positive and nice but it is very early in the season."
Chelsea went into its game at St James' Park on the back of a nine-match unbeaten run in all competitions and got off to a good start. But Jose Mourinho's side paid for its missed chances as Newcastle secured a first home win in two months with goals from French duo Yoan Gouffran and Loic Remy.
"I don't need to lose a match to be aware of (how competitive the league is)," Mourinho said. "It is something I pass on to my players every game. I know exactly how it is. The race is there for everybody."
Following the Blues' slipup, City moved up to fourth place, a point behind Chelsea and Liverpool.
United raced into a three-goal lead within the first 22 minutes before Alexander Kacaniklic pulled a goal back for Fulham with a shot that deflected in off Rooney in the 65th.
United was less impressive in the second half after United manager David Moyes made three changes during the interval following a string of injuries. The Red Devils, who have won their last six Premier League meetings with Fulham, stayed eighth in the table, two points behind City.
"It's always been my team since I've taken over from Alex Ferguson, 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," said Moyes, who replaced Ferguson this summer. "The players have great habits from the previous manager and they have a winning mentality which I see every day."
In other matches, goalkeeper Asmir Begovic scored a bizarre goal after 13 seconds in Stoke City's 1-1 draw with Southampton, while Sunderland had two men sent off in a 1-0 defeat at Hull City. Last-place Crystal Palace lost 2-0 at West Bromwich Albion, and West Ham was held to a goalless draw by Aston Villa.
City dropped England keeper Joe Hart after high-profile mistakes for club and country, and his replacement Costel Pantilimon enjoyed a quiet afternoon in his Premier League debut against Norwich.
Manuel Pellegrini's team cruised. Bradley Johnson scored an own goal to put City in front. Silva, Matija Nastasic and Alvaro Negredo then slotted home before the interval and Yaya Toure scored with a curled free kick in the 60th. Sergio Aguero and Edin Dzeko completed the rout.
"We were very unhappy when we lost against Chelsea (last weekend), we didn't deserve to lose that match — we dominated possession. So we continued playing the same way," Pellegrini said. "We won against Newcastle in the cup in midweek and I thought today we had a really good match. Norwich did not have a chance to score, we scored seven and could have scored more."
On a windy day at Britannia Stadium, Begovic scored almost immediately with a kick from his own area that bounced before flying into Artur Boruc's goal.
Southampton levelled in the 42nd as James Ward-Prowse crossed from the right for Jay Rodriguez to head home his third goal in his last four league appearances.
Against Sunderland, Hull took the lead after 25 minutes, thanks to an own goal by Carlos Cuellar. Another setback followed when Sunderland goalkeeper Kieren Westwood had to be replaced by Vito Mannone in the 43rd due to a neck injury.
However, much worse was to come for Sunderland's new manager, Gus Poyet, in first-half stoppage time, as Lee Cattermole picked up a straight red for a bad challenge on Ahmed Elmohamady and Andrea Dossena was dismissed for a stamp on David Meyler.