Arsenal reestablished a five-point lead at the top of the Premier League as the Gunners overcame 10-man Chelsea 2-1 on Sunday, while Benjamin Sesko fired Manchester United up to third with victory over Crystal Palace.
Manchester City relied on the latest goal from recently signed forward Antoine Semenyo to secure a win that kept the pressure on Arsenal in the Premier League title race.
Benjamin Sesko is yet to start in Carrick's six matches in charge but has come off the bench to net in three of his last four appearances with vital goals.
Arsenal's Premier League title challenge suffered a major blow as they squandered a two-goal lead and conceded a stoppage-time equaliser in a damaging 2-2 draw at rock-bottom Wolves.
Arsenal missed the chance to extend their Premier League lead to six points as Brentford rattled the Gunners in a 1-1 draw on Thursday to give Manchester City hope in the title race.
Manchester City beat Fulham 3-0 to close in on Arsenal at the top of the Premier League on Wednesday, as Liverpool inflicted Sunderland's first home defeat of the season to ease the pressure on Arne Slot.
Manchester City can ramp up the pressure on Premier League leaders Arsenal by cutting the gap at the top to just three points when they face Fulham on Wednesday.
Erling Haaland's stoppage-time penalty earned Manchester City a dramatic 2-1 win at Liverpool on Sunday to reduce Arsenal's lead at the top of the Premier League back to six points.
Bryan Mbeumo and Bruno Fernandes scored in each half at Old Trafford in a game that saw Spurs reduced to 10 men after captain Cristian Romero was sent off in the 29th minute.
Michael Carrick said Manchester United must not rush their choice of a permanent new manager after insisting nothing has changed about his own job prospects.