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.
Semenyo, who has scored 10 goals and been one of the best attackers in English soccer this season, has moved in a deal worth a reported 65 million pounds ($87 million) and on a 5 1/2-year deal.
Arsenal's Gabriel Martinelli aimed the ball at Liverpool defender Conor Bradley and pushed him off the field despite the latter being injured in the dying moments of their Premier League clash.
Nuno Espirito Santo insisted troubled West Ham can still avoid relegation after Morgan Gibbs-White's late penalty fired Nottingham Forest to a crucial 2-1 win on Tuesday.
Rodri said his return to fitness is a "gift" despite the disappointment of Manchester City dropping two points late on in a 1-1 draw against managerless Chelsea on Sunday.
Liverpool were held to a dramatic 2-2 draw by Fulham on Sunday as Harrison Reed scored a stunning stoppage-time equaliser just moments after Cody Gakpo netted for the Reds.
Aston Villa's 11-game winning streak in all competitions was brought to a shuddering halt with a 4-1 defeat at the Emirates on Tuesday, raising doubts about their ability to maintain a title charge.
Thomas Frank said the "boring Tottenham" taunts from his own club's fans were understandable after they were held to a dour 0-0 draw by Brentford on Thursday.
Manchester City trail Arsenal by four points at the top of the Premier League after failing to end Sunderland's unbeaten home record in a 0-0 draw on Thursday, while Liverpool were also held by Leeds.
Chelsea manager Enzo Maresca is facing an uncertain future at Stamford Bridge as the clubs poor run in the Premier League 2025-26 has raised serious concerns over his position.