The Reds returned to winning ways and earned a first victory at Goodison Park since 2011 thanks to goals from Morgan Schneiderlin, the recalled Ander Herrera, and Wayne Rooney.
It was the perfect way for United to return to league action following the international break and a chastening 3-0 defeat at Arsenal last time out.
The result ensured we continue to keep pace with the chasing Premier League pace, and, going into next weekend's massive derby clash, we sit two points behind City and level on points with the second placed Gunners.
Saturday's match was tinged with emotion at the news that Toffees legend Howard Kendall, former Everton player and manager, had died at the age of 69.
The players wore black armbands as a mark of respect and there was a minute's applause prior to kick off in a match that saw Louis van Gaal make four changes to his XI, with recalls for Phil Jones, Marcos Rojo, Schneiderlin and Herrera.
A slow start had cost United at Arsenal and the manager had demanded a much-improved opening on Merseyside.
He got his wish, too, as the Reds went ahead after 18 minutes when Schneiderlin drilled in his first competitive goal after good build up from Chris Smalling and Rojo.
Four minutes later, Herrera doubled the lead when the Spaniard burst into the area and nodded in a fine Rojo cross past former United stopper Tim Howard.
David de Gea saved well from Ross Barkley on the stroke of half-time before he brilliantly denied Romelu Lukaku with an outstretched foot shortly after the resumption.
Jesse Lingard replaced Juan Mata at the break, and the academy graduate was soon needed in defence as he headed away James McCarthy's dangerous cross as the hosts belatedly applied some pressure.
United stood firm, though, and put the result beyond any doubt just after the hour mark when Schneiderlin picked out the impressive Herrera, who in turn played in Rooney who fired in to score against his former club away from home for the first time since 2007.
Barkley went close and substitute Arouna Kone forced a save from De Gea, but United consolidated an excellent win, another clean sheet and three more deeply satisfying points.
United Faithful Man of the Match: Ander Herrera
Overall team performance: 8/10