Argentina's Hernan Crespo headed an 88th minute winner to give Chelsea a 2-1 victory at Middlesbrough, while Juan Pablo Angel equalised in Aston Villa's 1-1 draw with Bolton Wanderers in the premier league on Sunday.
Colombian Angel, however, had a penalty saved four minutes from time by Bolton's Finnish goalkeeper Jussi Jaaskelainen.
Chelsea, determined to make amends for their midweek home defeat by Besiktas of Turkey in the Champions League, stayed third in the standings.
The London club are one point behind leaders Arsenal and level with Manchester United, who both won on Saturday, and also have a game in hand.
Villa and Bolton are 13th and 15th respectively, both with eight points from eight games and 12 adrift of Arsenal.
Crespo scored his third goal in five games for Chelsea in English and European competition, rising to nod home from a tight angle after Damien Duff's cross to the far post.
The Argentine made up for a bad miss 11 minutes earlier when he robbed Boro captain Colin Cooper but shot straight at Mark Schwarzer, hitting the advancing keeper squarely in the face.
Man-of-the-match Duff also set up Chelsea's opening goal in the 17th minute for Iceland's Eidur Gudjohnsen, who fired a low shot inside Schwarzer's right hand post from the Ireland international's defence-splitting pass.
Chelsea had other first half chances when central defender John Terry headed Frank Lampard's free kick against the bar and Schwarzer had to dive sharply to his left to turn away Jesper Gronkjaer's shot.
Middlesbrough equalised through Szilard Nemeth virtually from the restart when the Slovakian forward took a ball from midfielder Gaizka Mendieta after a stumble by Chelsea defender Robert Huth.
Much-improved Boro were unlucky to lose and conceded their first goals in four matches. They had the better of the second half and were denied on several occasions by the goalkeeping of Chelsea's Carlo Cudicini.
"I still can't believe it, it just shows you this is a cruel game," Boro manager Steve McClaren said.
"We had a fantastic performance by the players, we deserved something for it," he told Sky Sports.
At Villa Park, Bolton took the lead 53 seconds into the second half when midfielder Kevin Nolan shot inside the far post from a headed pass by Kevin Davies, beating Dutch substitute keeper Stefan Postma who had yet to touch the ball after replacing injured Thomas Sorensen at the interval.
Angel equalised with his fourth league goal of the season when he shot from the edge of the box into the top right corner after the ball was laid off by midfielder Lee Hendrie.
Bolton manager Sam Allardyce said he was especially pleased that his side had scored their first away goal of the season.
"(Finishing) has been one of our problems all season that we have to try and rectify but I'm very pleased that we have broken that duck and Kevin, playing further up for us today, stuck it in the back of the net for us and gave us a lot of confidence.
"Both teams, particularly in the second half, had a number of chances to actually win the game but we both failed to take them," he said.
"That's probably the reason why we are where we are in the table at the moment."
Villa defender J Lloyd Samuel later hit the post with a volley from a corner before the penalty was awarded against Bolton's Spanish defender Ivan Campo for a foul on Angel.
Jaaskelainen dived to his left to push away the Colombian's spot kick.
"We had a chance to take the three points which we probably wouldn't have deserved," said Villa manager David O'Leary.
A bried summary of the matches played on Saturday:
FULHAM 2 -0 LEICESTER CITY
Fulham maintained their impressive start to the season with their first victory over Leicester since 1979 thanks to Luis Boa Morte's double.
Boa Morte gave the Londoners the lead in the 36th minute after Steed Malbranque's shot hit the woodwork.
He grabbed his second, and his fifth of the season, in the 73rd minute after a superb pass from Malbranque. Defeat left Leicester in the relegation zone.
LEEDS UNITED 2 -1 BLACKBURN ROVERS
Leeds manager Peter Reid's traumatic week ended on a high as his side ended a run of three consecutive defeats to move out of the relegation zone.
Reid, who received a much-publicised vote of confidence on Thursday, watched his side take the lead in the 11th minute with a close-range Seth Johnson finish.
Midfielder Johnson then rewarded a rejuvenated Leeds with a second goal after 26 minutes. Dino Baggio scored his first goal for Blackburn after 86 minutes but it could not deny Leeds their first home win of the season.
LIVERPOOL 1 - 2 ARSENAL
A stunning Robert Pires strike kept Arsenal top of the table as they came from behind to claim all three points at Anfield.
Liverpool dominated early on and Harry Kewell gave them a deserved lead after 14 minutes with an emphatic low finish from the edge of the penalty area.
Arsenal, without the injured Patrick Vieira and Freddie Ljungberg, levelled on the half hour when Edu's header from a Pires free kick deflected in off Sami Hyypia's foot.
Arsenal, still unbeaten in the league this season, improved in the second half and sealed the points in the 68th minute when Pires drifted in from the left to curl a delightful shot past Jerzy Dudek.
MANCHESTER UNITED 3 - 0 BIRMINGHAM CITY
Birmingham arrived at Old Trafford having conceded just two goals in the league this season and the champions found Steve Bruce's side hard to play against at Old Trafford.
The breakthrough came in the 36th minute when Ruud van Nistelrooy converted from the penalty spot after City goalkeeper Maik Taylor was sent off for bringing down Paul Scholes.
Scholes made the points safe after 57 minutes with a drilled shot past substitute keeper Ian Bennett before Ryan Giggs added a late third to condemn Birmingham to their first defeat of the season.
NEWCASTLE UNITED 1 - 0 SOUTHAMPTON
Alan Shearer's 250th career league goal put struggling Newcastle on the way to their first premier league victory of the season.
The former England striker pounced just before halftime, drilling in a low shot against his former club.
Craig Bellamy wasted several good chances to increase Newcastle's lead and they had to endure a tense final few minutes as Southampton looked to snatch a point.
PORTSMOUTH 1 - 2 CHARLTON ATHLETIC
Portsmouth slipped to their third straight league defeat as the early-season optimism evaporated at Fratton Park.
Teddy Sheringham headed his sixth goal of the season from Tim Sherwood's corner to put the home side ahead in the 34th minute.
Charlton deservedly equalised after 77 minutes through Jon Fortune's close-range effort and the London club stole the points in the dying seconds when South African striker Shaun Bartlett rose to head in substitute Paolo di Canio's corner.
TOTTENHAM HOTSPUR 3 - 0 EVERTON
Tottenham caretaker manager David Pleat made it three games unbeaten since Glenn Hoddle was sacked.
Everton, without a win over Spurs since 1997, rarely looked like ending that jinx, and the home side took the lead through Frederic Kanoute's superb dipping shot from 30 metres.
Gustavo Poyet doubled the advantage with a header straight after the interval before Robbie Keane added a third three minutes later.
Everton manager David Moyes sent on substitute Wayne Rooney, but the teenage England striker's main contribution was to receive a yellow card.
WOLVERHAMPTON WANDERERS 1 - 0 MANCHESTER CITY
The long wait is over for Wolves fans after they finally chalked up a victory on their return to the big time.
Colin Cameron proved the hero, heading the winner after 75 minutes from a cross by Henri Camara and scoring Wolves's first home goal in the top flight since 1984.
City's Sun Jihai almost ruined the party in the final minute, but his goalbound header was brilliantly saved by Wolves keeper Michael Oakes.