Angel di Maria opened the scoring with a wonderful finish before David de Gea had to save a penalty from Leighton Baines. Steven Naismith levelled the scores, but Falcao scored his first goal for Manchester United, which proved to be the winner after David de Gea produced a pair of sensational saves late on to save the points.
United started brightly, with Antonio Valencia proving surprisingly capable in the middle, and had a few chances early on, with Falcao guilty of missing a couple of chances after fine work from Di Maria. The Argentinian was looking like United's most dangerous player by a significant margin, and after a fine move he collected Juan Mata's knock-down to put a brilliant curling finish past Tim Howard from the edge of the area.
United were looking dominant, but suddenly Luke Shaw gave away a penalty by chopping down Tony Hibbert. Leighton Baines, who has never missed a Premier League penalty, stepped up to take it, but his poor effort was kept out by De Gea.
United's lead didn't last too long, however, as Steven Naismith soon took advantage of an excellent Baines cross to level the scorelines, and United were suddenly looking uncomfortable. But Falcao, despite having a poor game up until that point, soon put them back in front by turning Di Maria's effort over Tim Howard and into the back of the net.
Everton managed another late rally, however, but United were able to hold firm to deny them. Tyler Blackett produced one fine block, which was followed up by an excellent save from David de Gea to deny Leon Osman. And the Spaniard saved his best for last, as Bryan Oviedo volleyed through a crowd in the area, only for De Gea to tip it over the bar.