Lionel Messi went top of the scoring chart in Europe's top five leagues and Ole Gunnar Solskjaer won his sixth match in a row.
In another action-packed Premier League weekend, Maurizio Sarri called out his players, while Dele Alli went down with another injury for Spurs.
Rashford, 21, made his 150th Man United appearance in the 2-1 win over Brighton, reaching the mark at a younger age than both Rooney and Ronaldo.
Sarri took the remarkable step of publicly accusing his players of being "extremely difficult to motivate" after Saturday's loss to Arsenal.
Darmian's deal was due to expire at the end of the season but United have triggered a one-year option that will end in 2020.
Tottenham struggled at Fulham without the injured Harry Kane and absent Son Heung-Min, and with Dele Alli now potentially hurt, it could get worse.
Tottenham boss Mauricio Pochettino has said he is concerned by Dele Alli's injury after seeing the player substituted clutching his left hamstring.
Tottenham pulled off a last-gasp win against Fulham, but it wasn't thanks to Harry Kane backup Fernando Llorente, who almost cost them the points.
Tottenham struggled in their first game without Harry Kane but edged past struggling Fulham thanks to a stoppage time winner from Harry Winks.
|West Ham United||23||9||4||10||-4||31|
|Brighton & Hove Albion||23||7||5||11||-7||26|