Midfielder Herrera fired home with his left foot just before the break at Old Trafford on Saturday to put Louis van Gaal's side on course for a fifth consecutive top-flight win.
Rooney then doubled United's lead with a sublime finish before Herrera added his second goal in stoppage time to seal victory after Christian Benteke had given Villa brief hope immediately after Rooney's stunner.
The home side were deserved winners and are now a point above City - who play Crystal Palace on Monday - ahead of next Sunday's derby with the champions and a clash with leaders Chelsea the following weekend.
Defeat for Villa leaves them without a victory over United in their last 12 attempts and Tim Sherwood's side are now just three points ahead of third-bottom QPR, who beat West Brom on Saturday and travel to Villa Park on Tuesday.
Villa were struggling to live with the home side's intensity and Juan Mata's goal-bound shot was well blocked by Clark after Ashley Young had tormented his former club with a great run down the left.
Rojo almost marked his recall with a goal 23 minutes in, but the Argentina international's long-range strike was brilliantly tipped over the crossbar by the agile Brad Guzan.
Marouane Fellaini ought to have doubled United's lead just after the hour mark, but the unmarked Belgium midfielder headed the ball down into the ground and Guzan palmed the effort behind.
Rooney did give them breathing space 11 minutes from time, though, sticking out his left leg to control substitute Angel Di Maria's cross before swivelling to fire into the top corner of the net with his right boot.
