Manchester United took advantage of a slip-up from Manchester City to close to within 13 points of the league leaders with a 2-0 win over Huddersfield Town at Old Trafford.
Earlier, City dropped points for just the fourth time in the Premier League this season in a 1-1 draw at Burnley as Johann Berg Gudmundsson’s equaliser eight minutes from time cancelled out Danilo’s spectacular opener for City.
Mourinho had called on his players to bounce back from the midweek defeat at Spurs in style, but the Red Devils had to wait until 10 minutes into the second half to make the breakthrough when Lukaku got across his marker to volley home Juan Mata’s cross from the left for his 19th goal of the season.
New boy Alexis Sanchez capped his home debut with a goal 21 minutes from time when he was brought down just inside the area, and the Chilean tapped home the rebound after Jonas Lossl had saved his initial effort from the penalty.
Leicester City missed the magic of star man Riyad Mahrez as they failed to beat Swansea City at home in a 1-1 draw at the King Power Stadium, Argentine Federico Fernandez cancelling out Jamie Vardy’s opener.
In a big day in the relegation dog fight, Southampton snapped a 12-game winless run with a 3-2 win at West Brom, while Brighton also bagged their first league win in seven games thanks to goals from Glenn Murray, Jose Izquierdo and Pascal Gross to beat West Ham 3-1.
Bournemouth moved up to ninth as they came from behind to beat Stoke City 2-1 through strikes from Josh King and Lys Mousset in the final 20 minutes to drop Stoke back into the drop zone.
In the late kickoff, Pierre-Emerick Aubameyang scored a debut goal and Aaron Ramsey his first hat-trick as Arsenal thumped a disorganised Everton 5-1.