Phil Jagielka's stoppage-time equaliser meant that Liverpool have kept just one clean sheet in their last 12 Premier League outings.
Even so, despite having secured a late point, Everton are without a victory at Anfield since September 1999.
As for the hosts, Steven Gerrard took his Merseyside derby Premier League goal tally to nine - no player has scored more in this fixture.
Chelsea 3-0 Aston Villa
From their last eight Premier League home encounters against Villa, Chelsea have found the net on 30 occasions.
One of their goalscorers - Diego Costa - extended his goals return to eight in six outings this season.
Paul Lambert's Villa went into the contest as the only Premier League side to have not conceded a goal away from home.
Crystal Palace 2-0 Leicester City
Mile Jedinak had previously scored one goal in his last 42 Premier League appearances, but after he found the net against Leicester, the Australian has scored two in two.
Palace boss Neil Warnock has gone four top-flight encounters without losing for the first time since he was in charge of Sheffield United back in 2006.
The last time that these two sides met in the Premier League was back in April 1998.
Hull City 2-4 Manchester City
Man City frontman Sergio Aguero scored his 10th away goal in 12 Premier League outings at the KC Stadium.
Frank Lampard also found the net for City, which means that he has scored in back-to-back Premier League fixtures for the first time since February 2012.
Hull have scored twice in each of their last four encounters in all competitions, but have won none of them.
Manchester United 2-1 West Ham United
Man United skipper Wayne Rooney was red-carded for the first time in the Premier League since he was given his marching orders away at Fulham in March 2009.
His teammate, Radamel Falcao, laid on a second assist for Robin van Persie in as many matches. The Colombian had only recorded one assist in the previous three seasons with Atletico Madrid and Monaco.
The Hammers have never scored more than one goal at Old Trafford during the Premier League era.
Southampton 2-1 Queens Park Rangers
In his last 63 league outings for Feyenoord and Southampton, Graziano Pelle has found the net on 54 occasions.
Up the other end, no Premier League side have conceded fewer goals than the Saints, who have shipped just four this season.
Charlie Austin's goal for QPR was the first that the West Londoners had scored away from home since their return to the top flight.
Sunderland 0-0 Swansea City
The visiting Swans had not previously drawn any of their Premier League encounters prior to their visit to the Stadium of Light.
Meanwhile, Sunderland have now drawn a league-high five encounters this term.
The hosting Black Cats, under the management of Gus Poyet, are on an winless run of seven Premier League matches.
Arsenal 1-1 Tottenham Hotspur
Alex Oxlade-Chamberlain, who scored Arsenal's equaliser, took his goals tally for the Gunners to 10, all of which have been scored at the Emirates Stadium.
Tottenham's goal was scored by Nacer Chadli, who now has four in his last five Premier League appearances. Last season, the Belgian scored just once in 24 outings.
Spurs have won just one of the last 22 North London derbies that Arsenal have hosted.
West Bromwich Albion 4-0 Burnley
Graham Dorrans became the second West Brom player after Peter Odemwingie to provide two assists and score a goal in one Premier League match.
Heading into this fixture, the Baggies had only scored three times in five games.
As for Sean Dyche's Burnley, they are still seeking their first victory of the season, having drawn three encounters and lost the other three.
Stoke City 1-0 Newcastle United
Peter Crouch's goal was the 600th that Newcastle have conceded away from home in the Premier League.
Goals have been hard to come by for the Magpies of late. From their 25 Premier League outings in 2014, they have found the net on only 19 occasions.
The victory was the first of the season at the Britannia Stadium for the hosts.
