Yaya Toure came off the bench to curl in a free kick from 20 yards -- his third such goal of the season -- and Jovetic netted again from close range in the 83rd after Ryan Shotton made a mess of a clearance.
Jesus Navas rounded off the scoring three minutes later when he broke through and fired a low shot past goalkeeper Lee Nicholls.
At Villa Park, 42-year-old American goalkeeper Brad Friedel had little to do on his return to his own club as the Tottenham attack shone.
