Manchester United have won all five matches since Ole Gunnar Solskjaer took the helm at Old Trafford following the sacking of Jose Mourinho.
A third consecutive victory since Solskjaer took caretaker charge until the end of the season.
The win helped Liverpool move one point ahead of Manchester City in the Premier League points table.
Raheem Sterling inspired Manchester City to a 3-1 win over Bournemouth, while Crystal Palace clinched a crucial 2-0 victory over Burnley.
Manchester City host Eddie Howe's Bournemouth in the Premier League on Saturday.
Arsenal have been revitalised since Unai Emery replaced Arsene Wenger in the close-season.
It was Manchester United's third victory in their last four Premier League games.
Bournemouth vs Manchester United, Premier League 2018: Marcus Rashford scored the winner for Man Utd.
Mauricio Pochettino's men will host another two home fixtures against Cardiff and Liverpool at Wembley.
Bournemouth have signed Diego Rico from Leganes, subject to the defender receiving international clearance, the English Premier League club said Tuesday.
Jose Mourinho admitted Manchester United had given him an FA Cup semi-final selection dilemma after their 2-0 win at Bournemouth on Wednesday.
Harry Kane limped off with his side trailing 1-0 at Bournemouth on Sunday, before Pochettino's men bounced back to win 4-1
Tottenham Hotspur move above Liverpool into third in the Premier League, but it was a bittersweet victory with concerns over Harry Kane's fitness.
Tottenham Hotspur ensured the focus switched back to the pitch, stunning Jose Mourinho's Manchester United with a performance full of attacking verve in a 2-0 win.
Eden Hazard quietened the debate surrounding Antonio Conte's future with the second-half goal that secured a 1-0 win at Bournemouth on Saturday.
Raheem Sterling celebrated his goal by throwing himself into the away section and was shown a second yellow card by referee Mike Dean.
Everton beat West Brom 3-0, Hull City defeated Swansea City 2-1 and Bournemouth edged past West Ham 3-2 in the Premier League on Saturday.
Zlatan Ibrahimovic led with his right elbow as he clattered into Mings while the duo challenged for an aerial ball just before half-time.