Angel Di Maria put the Red Devils in front in the first half and Leighton Baines had a penalty saved before Steven Naismith's equaliser but the Colombian had final say
Angel Di Maria curled home the opening goal from the edge of the box midway through the first half but the Red Devils had to survive multiple scares, with Luke Shaw conceding a penalty just before half-time by bringing down Tony Hibbert.
David de Gea saved Leighton Baines's attempt from the spot but Everton struck back in the 55th minute through a brilliant headed goal by Steven Naismith, assisted by the left-back.
|VIEW FROM OLD TRAFFORD
|By Peter Staunton
For a moment it looked like Manchester United would win a game comfortably. They went in leading at half-time and David de Gea saved a penalty.
By the end, however, they had the Spaniard to thank for all three points after he made a string of saves to keep Everton out late on.
United should have strolled this one but were made to work hard due to the Everton equaliser by Steven Naismith - then the familiar nerves began jangling. Deeper they retreated into their own territory as the Toffees seized the initiative but the lead given to them by Radamel Falcao proved sufficient, just.
At the heart of it was Angel Di Maria, again United's best performer. He scored one and assisted another in a masterclass. They had to work harder than expected but these are three welcome points for United all the same.
The result was a huge boost to United ahead of a two-week international break, during which Van Gaal will hope that some of his injured players – including Shaw, following his 70th-minute withdrawal – will regain full fitness. Defeat for Everton, meanwhile, extends their winless streak to five games in all competitions.
Juan Mata deputised for the suspended Wayne Rooney, with Robin van Persie taking the captain's armband, and Antonio Valencia came in for injured midfielder Ander Herrera. Everton made two alterations from their 1-1 draw at Liverpool, Steven Pienaar and Aiden McGeady replacing Kevin Mirallas and James McCarthy.
United began confidently in attack, Falcao forcing an early save from Everton goalkeeper Tim Howard with a diving header from Shaw's cross. Van Persie was next to threaten when turning an effort just over following a powerful Di Maria centre.
The hosts continued to look the more dangerous, even if Everton were enjoying the lion's share of possession.
Roberto Martinez's side found themselves behind in the 27th minute, Di Maria continuing his fine form since moving to Old Trafford from Real Madrid in August. After Phil Jagielka had brilliantly hooked Rafael's cross clear, the ball fell to Mata, who squared for the Argentina international to curl beyond Howard.
Howard was called into action again soon after, turning Di Maria's deflected free kick over the crossbar.
United were fortunate to head into the break ahead, though, with De Gea denying Baines from the penalty spot in first-half stoppage time after Shaw had felled Tony Hibbert.
Van Gaal's men were pegged back in the 55th minute when Naismith met Baines's superb cross with a clever diving header to haul the sides level.
Suddenly in the ascendancy, Everton pressed forward further, with Jagielka seeing a header cleared off the line after meeting Baines's corner, but United found a response, Falcao producing a smart finish to convert Di Maria's effort.
Nervy moments followed for the home side, De Gea denying Leon Osman with a stunning one-handed stop.
De Gea's heroics did not end there, the Spaniard once more producing a stunning save to turn over Bryan Oviedo's volley after Tyler Blackett had superbly blocked Gareth Barry's strike.