Charlie Adam put the hosts in front with a deflected effort, then smashed home an excellent second to settle the 2-1 victory after Robin van Persie had levelled straight after the break.
Moyes started Mata, Rooney and van Persie together for the first time, but it was the first half injuries to whose Evans and Jones that ultimately contributed to United’s eighth defeat of the season.
Earlier on Saturday, Alan Pardew was left alone to face a furious backlash as Newcastle suffered another humbling derby defeat by Sunderland.
Sunderland’s third derby victory on the trot was secured by first-half goals from Fabio Borini and Adam Johnson, who struck for the seventh time in as many games, and Jack Colback’s late strike.
Leandro Bacuna gave Villa a shock lead but Everton ramped up the pressure in the second half and got their reward when Naismith struck 16 minutes from time.
Cardiff’s new boys made an instant impact as Wilfried Zaha and Kenwyne Jones enjoyed dream debuts in a 2-1 win over Norwich.
Robert Snodgrass gave Norwich the lead in just the fifth minute but substitute Wilfred Zaha teed up Craig Bellamy for the equaliser just after the break, with Jones firing home the winner at the second attempt just over a minute later.
Andy Carroll twice set up goals for Kevin Nolan before being sent off as ten-man West Ham beat Swansea to ease their relegation predicament.
The England striker twice provided cushioned headers for Nolan to score in a 2-0 win at Upton Park but later received a straight red card for an altercation with Chico Flores. West Ham have immediately appealed against the dismissal.
Shane Long’s first goal for Hull saw them claim their first point of the year from a 1-1 draw which ended Tottenham boss Tim Sherwood’s perfect away record in the league.
Former West Brom striker Long put the Tigers ahead 12 minutes into his home debut but Paulinho’s powerful 61st-minute strike drew Spurs level and salvaged a share of the spoils.
Elsewhere, the renewed optimism brought by Fulham’s late flurry of transfer activity quickly evaporated as Southampton became the eighth side to take three points at Craven Cottage this season.
Goals from Adam Lallana, Rickie Lambert – who scored his 100th league goal for Saints – and Jay Rodriguez ruthlessly exposed Fulham’s soft underbelly and clinched a comfortable 3-0 away win.
Recent arrivals Lewis Holtby and William Kvist started for the Cottagers but were unable to stop their new club slipping to the bottom of the Premier League table.