Their fellow challengers Chelsea and Manchester City also picked up victories, but Manchester United and Liverpool both dropped points from their encounters with Tottenham Hotspur and Hull City respectively.
Here, Sports Mole has picked out the 11 players who we believe had the biggest impact on the weekend's action.
Wojciech Szczesny (Arsenal)
The Pole may not have had too much to do at the Cardiff City Stadium, but his save from Fraizer Campbell with the score at 1-0 in Arsenal's favour has been viewed, quite rightly, as a key moment.
Bryan Oviedo (Everton)
Everton fans could have been forgiven for fearing that they would miss Leighton Baines, but Oviedo allayed any fears with a performance that the England international would have been proud of, which he rounded off with a goal.
Curtis Davies (Hull City)
Facing up to the prospect of marking Liverpool centre-forward Luis Suarez is no doubt a daunting one, but Davies appeared to take it in his stride as he played a key role at the heart of Hull's defence.
John Terry (Chelsea)
Excluding penalties, no defender has scored more Premier League goals than the Chelsea skipper. He netted another important one against the Saints, which put the Blues 2-1 up.
Seamus Coleman (Everton)
Like his teammate Oviedo, full-back Coleman got his name among the scorers for Everton. The Republic of Ireland international proved to be a constant threat down the right flank.
Gerard Deulofeu (Everton)
The young Spaniard had been dubbed the brightest prospect to come through the Barcelona academy since Lionel Messi. His loan spell at Goodison Park had been a stuttering one, but he showed that the plaudits could well be correct with a goal and an assist against Stoke.
Aaron Ramsey (Arsenal)
The Welshman took his Premier League tally for the season to eight goals with a brace against his former club. His lack of celebration was respected by the home supporters, who applauded the midfielder.
Mousa Dembele (Tottenham Hotspur)
Manager Andre Villas-Boas opted to start with Dembele following a spell on the bench and he was rewarded with a positive display by the Belgian. He provided his side with a real physical presence that Manchester United found difficult to deal with.
Samir Nasri (Manchester City)
Nasri recently admitted that he was not at his best last season, but the attacking midfielder displayed his ability with a two-goal performance against Swansea City at the Etihad Stadium.
Wayne Rooney (Manchester United)
The England international continued his revival under the guidance of David Moyes by scoring both of United's goals at White Hart Lane. He also played the ball through for Danny Welbeck, who was then brought down by Hugo Lloris for the penalty.
Demba Ba (Chelsea)
He may only have been introduced during the break, but without Ba's influence, the Blues may have struggled to pick up a positive result. He caused numerous problems to the Southampton rearguard and made sure of the points in the closing stages by scoring his team's third goal.
Numpty of the week
Martin Skrtel: It was a match for the Liverpool defender to forget at Hull City. The home side's first goal, which was struck by Jake Livermore, deflected into the net off the Slovakian. Then, in the closing stages, he headed a shot from Tom Huddlestone that was going wide into his own net.
Goal of the week
Sandro (Tottenham Hotspur) vs. Manchester United: The Brazilian had only previously scored two goals for Spurs, but this will probably be the most memorable. Having turned Tom Cleverley, he sent a swerving effort from 25 yards out into the top corner of David de Gea's net.