Premier League leaders Chelsea conserved their three-point advantage by beating Aston Villa 3-0 on Saturday, while Wayne Rooney was sent off as Manchester United edged West Ham United.
Having drawn 1-1 at champions Manchester City last weekend, Chelsea continued their unbeaten start to the season with a straightforward win over Villa at Stamford Bridge.
Willian set up Brazilian countryman Oscar to steer home Chelsea's opener in the seventh minute before Diego Costa scored his eighth goal in six Premier League games with a glancing header.
Costa also played a role in Chelsea's third goal with a right-foot drive that Brad Guzan could only push straight at Villa defender Aly Cissokho, enabling Willian to stab home from close range.
"Even during the period the game was 1-0, when it could be open, it was always closed because we controlled the game," said Chelsea manager Jose Mourinho. "The result was a consequence of our dominance."
Southampton remain Chelsea's closest rivals after winning 2-1 at home to Queens Park Rangers, with Ryan Bertrand and Graziano Pelle finding the net either side of a Charlie Austin effort.
United climbed six places to seventh, eight points below Chelsea, after seeing off West Ham 2-1 at Old Trafford, but their victory was overshadowed by the red card shown to captain Rooney.
Injury problems forced United manager Louis van Gaal to give a debut to 19-year-old centre-back Paddy McNair.
But they took a fifth-minute lead when Rooney swept home Rafael da Silva's cross to become the outright third-highest scorer in Premier League history with 176 goals; one more than Thierry Henry.
Radamel Falcao set up Robin van Persie to rattle in United's second goal mid-way through the first half, but Diafra Sakho reduced the arrears for West Ham by nodding in after Enner Valencia's header hit the bar.
Rooney was shown a straight red card in the 59th minute for hacking down the fleeing Stewart Downing - his first club dismissal since March 2009 - but United's 10 men held on to secure victory.
"I call it a professional foul," said Van Gaal. "I've seen them a lot of times, but the referee makes another decision. But you can't change it."
Lampard on target again
Meanwhile, champions Manchester City withstood a fightback by Hull City to record a 4-2 win at the KC Stadium that saw them climb to third.
With Willy Caballero preferred to Joe Hart in goal by City manager Manuel Pellegrini, the visitors went 2-0 up through a hooked finish from Sergio Aguero and a fine 22-yard strike by Edin Dzeko.
However, a pair of blunders by City's new centre-back Eliaquim Mangala allowed Hull back into the game.
The France international headed Liam Rosenior's cross into his own net in the 21st minute and then conceded a penalty with a high boot on Abel Hernandez, who converted from 12 yards to level the scores.
But after Yaya Toure had hit the post, David Silva released Dzeko to restore City's lead in the 68th minute before substitute Frank Lampard side-footed in his fourth goal in three games late on.
Elsewhere, a close-range strike 16 minutes from time by Alex Oxlade-Chamberlain earned Arsenal a 1-1 draw at home to Tottenham Hotspur in the north London derby.
Arsenal lost Mikel Arteta and Aaron Ramsey to injury before half-time and then saw Nacer Chadli give Tottenham a 56th-minute lead.
But Oxlade-Chamberlain crashed home from Santi Cazorla's low cross to earn Arsenal a draw that left Arsene Wenger's side in fourth place and Spurs eighth.
"I'm frustrated because of the possession we had and the effort the players put in, and I'm frustrated with our set-pieces," Wenger told Sky Sports. "But we showed good spirit and determination."
Earlier, Everton captain Phil Jagielka scored a sensational 92nd-minute equaliser to earn his team a 1-1 draw against derby rivals Liverpool at Anfield.
Steven Gerrard had put Liverpool ahead with a second-half free-kick, but he was upstaged in injury time when his former England colleague Jagielka drove an exquisite half-volley into the top-right corner from 25 yards.
Liverpool manager Brendan Rodgers, whose side are without a win in three league games, said: "We were clearly the dominant side in the game, but sometimes you don't get what you deserve in football."
Quick-fire second-half goals from Fraizer Campbell and Mile Jedinak gave Crystal Palace a 2-0 win at home to Leicester City, while Angel Rangel was sent off for two yellow cards as Swansea City drew 0-0 at Sunderland.