Champions League holders Liverpool beat Sunderland 1-0 as Xabi Alonso scored through a free kick.
Villa are sixth, five points behind the leading pair after four matches but have won both home games.
Danny Welbeck, making his first appearance of the season as a late substitute, headed a stoppage-time winner to give Arsenal a 2-1 home win over league leaders Leicester City in the Premier League on Sunday.
Police said they had interviewed Lee Bowyer and Kieron Dyer after their on-pitch brawl during an English Premiership game earlier this month.
The United fans, who celebrated the victory at the end of the game with the manager and players, have not been the source of criticism of Solskjaer -- indeed the Norwegian has enjoyed strong backing from supporters who attend games at Old Trafford and those who travel away.
Christian Benteke wants to stay at Liverpool but is reluctant to commit his future to the Anfield club unless he gets more game time under manager Juergen Klopp. The former Aston Villa striker scored nine league goals during a mixed first season at the Merseyside club but made 15 of his 29 Premier League appearances from the bench. Benteke was signed by Klopp's predecessor, Brendan Rodgers, for 32.5 million pounds ($47.00 million) and under the German found himself behind Daniel Sturridge, Divock Origi and Roberto Firmino in the pecking order.
IMAGES from Premier League matches played on Saturday.
England's young forwards must consider leaving major clubs to play more regularly in their preferred positions and boost their chances of breaking into the national team, former Arsenal and England striker Ian Wright has said.
With City pulling out and Chelsea set to leave, while Liverpool's players posted a shared Twitter message saying they want no part of the new league, the ESL project looks doomed.
Burnley's seemingly doomed attempt to avoid relegation from the Premier League.
Liverpool moved into the top five of the English Premier League with a 2-1 victory at relegation-threatened Norwich City.
European champions Liverpool are second in their Champions League group - a point behind Napoli - and Klopp's side host Genk at Anfield.
The English Premier League champions won 1-0 at Newcastle United through a superbly struck volley by skipper Patrick Vieira.
Pierre-Emerick Aubameyang scored his first three goals for Barcelona in a 4-1 win at Valencia, but Inter Milan suffered a shock 2-0 home defeat by Sassuolo. Images from the football matches played on Sunday.
Arsenal will begin their quest to become the first club since 1886 to win the English FA Cup three years in succession.
Raheem Sterling scored a second-half hat-trick as leaders Manchester City beat Watford 3-1 on Saturday while Liverpool kept the gap at one point by overcoming Burnley 4-2 on Sunday.
Arsene Wenger gets another chance to finally beat his old nemesis and keep the Premier League title race alive for a little longer when Arsenal host leaders Chelsea on Sunday.
The points table of the English Premier League 2015-16 season.
Aston Villa will meet holders Arsenal in the FA Cup final next month.
But title rivals Chelsea and Manchester United were held in Saturday's Premiership matches.
With no European prizes left to chase this season, England's top clubs are focussed on winning the Premier League title, although that goal looks beyond all but Chelsea.
Diego Costa continued his rich vein of form as he helped leaders Chelsea to a 3-0 win over Aston Villa while Louis van Gaal enjoyed only his second Premier League win as Manchester United manager following a 2-1 victory against West Ham.
Images from the English Premier League matches played on Wednesday.
The Manchester United midfielders have knee injuries and will miss Champions League matches against Basel and Deportivo Coruna.
Images from the English Premier League matches on Saturday.
Robin van Persie will play no part in Manchester United's busy holiday programme after being ruled out for a month with a thigh injury, manager David Moyes said on Friday.
Wayne Rooney scored two first half goals to help send Manchester United to a 4-1 win over a spirited Aston Villa on Saturday, temporarily lifting the gloom surrounding David Moyes' dismal first term in charge.
Champions Arsenal eased to a comfortable 2-0 home win over Middlesbrough on Saturday, extending their lead at the top of the English premier league to two points.
The former beat Leeds United 4-1 while Manchester United got the better of Aston Villa 2-1 in the third round of the FA Cup.
News of all that's transpired on and off the football field.