Aided by Chris Smalling's sending off during a goalless opening period at the Etihad Stadium, Manuel Pellegrini's men took control after the interval as Sergio Aguero grabbed the decisive goal, his 10th in the league this season.
The Argentina striker's effort condemned United to a fourth successive league loss to their rivals for the first time since 1970 and ensured Louis van Gaal was defeated in his maiden all-Manchester clash.
That, combined with centre-back partner Marcos Rojo being withdrawn through injury in the 56th minute, proved crucial as the hosts took the points
Valencia was immediately tested, too, beaten by Aguero - who subsequently forced a first save from David de Gea.
But United responded quickly, Adnan Januzaj volleying just wide after being teed up by Robin van Persie's cushioned header.
A decisive moment came in the 38th minute, however, when Smalling - who had already picked up a cheap yellow card for impeding Joe Hart as the City goalkeeper attempted to punt downfield - flew into an ill-judged challenge on James Milner.
Van Gaal's woes were added to as injury forced Rojo off, leaving United to field a makeshift back four featuring Valencia, Michael Carrick and youngster Paddy McNair.
And soon after being denied another penalty, Aguero gave City a 63rd-minute lead by coolly side-footing home Clichy's pull-back after Yaya Toure had freed the left-back.
Navas rattled the outside of the post, while at the other end Di Maria was denied by Hart after a stunning burst from Rooney.
