Second half goals from Bryan Mbeumo and Patrick Dorgu sealed the win that had Manchester United fans singing in full voice and drowning out their fierce cross-city rivals.
Carrick's only full-time managerial experience was at second-tier Middlesbrough from 2022-25, where his reign ended after failing to secure promotion to the Premier League.
Michael Carrick was poised to become Manchester United interim coach on Tuesday after the Premier League giant turned to its former player to salvage its imploding season.
Cristiano Ronaldo was all praise for former Manchester United assistant manager Michael Carrick, who took over as caretaker manager of the club for three games after Ole Gunnar Solskjaer was sacked last month.
Michael Carrick exited Manchester United with a win as Cristiano Ronaldo surpassed 800 goals for club and country with a double to see off Arsenal 3-2 on Thursday.
Premier League: Liverpool manager Jurgen Klopp says Ralf Rangnick's expected arrival at arch-rivals Manchester United is "not good news for other teams" due to his vast experience and ability to organise teams.
Former Real Madrid boss Zinedine Zidane, Leicester manager Brendan Rodgers and Ajax coach Erik ten Hag have also been linked to take over as Manchester United's new manager.
Manchester United have sacked manager Ole Gunnar Solskjaer, a day after the club slipped to a humiliating defeat at Watford in the Premier League.
Michael Carrick has begun his new job as a member of manager Jose Mourinho's coaching staff, with this weekend's clash against Chelsea at Wembley his first assignment.
The 36-year-old veteran has been plagued by injury and illness concerns this season and has been limited to one appearance, in September's League Cup tie with Burton.