Manchester United returned to the Premier League's top four for the first time in more than a year as Radamel Falcao's first United goal proved decisive against Everton.
Angel Di Maria's calm finish gave the hosts a lead that survived to half-time as Leighton Baines saw a penalty saved.
Baines picked out Steven Naismith to nod in an equaliser and Falcao cleared a Phil Jagielka header off the line.
But Falcao stabbed in from Di Maria's shot to grab the winner.
Everton, who have won only one of their first seven league games, could easily have taken something from the game but Bryan Oviedo, who scored the winner in the fixture last season, was denied by a tremendous stoppage-time save from David De Gea.
The Spaniard also had to be alert to keep out a late Leon Osman effort but, while United will be concerned by their vulnerability under late pressure, the result and the three points were paramount.
Their first back-to-back league wins under Louis van Gaal carry the Dutchman's side into the Champions League qualification places for the first time since they drew with Chelsea in predecessor David Moyes' second league match in charge.
With the international break, their next game is not until 20 October when they are away to West Brom and Van Gaal will hope his new-look side can consolidate their form to ensure more comfortable afternoons at Old Trafford.