Manchester United secured consecutive Premier League wins for the first time this season as they beat Everton 2-1 at Old Trafford.

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.

But Radamel Falcao stepped up shortly afterwards to prod home his first United goal, which proved enough to give Louis van Gaal's side the points after De Gea made some outstanding late saves to preserve them.

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.