The Portuguese international struck in the 62nd minute to make it three goals in successive Sky Bet Championship games and settle a low-key encounter.
Norwich, who had lost six games out of seven before this one, were the better side throughout and had the chances to have won by a bigger margin, while Steve Bruce’s side never got out of first gear.
They failed to force John Ruddy into a save until injury-time, when the Canaries keeper comfortably kept out Jonathan Kodjia’s close range effort,
After a scrappy start, with frequent misplaced passes from both sides, Norwich finally produced the first effort on goal after 11 minutes, with Graham Dorrans’ shot from just outside the box being deflected wide by James Chester.
The Canaries gradually began to turn the screw and midway through the first half Martin Olsson tested Villa keeper Pierluigi Gollini with a low drive which he palmed into the path of Oliveira, whose close-range effort was smothered.
A dull opening period also saw Oliveira fail to make the most of an excellent ball into the danger area from Jonny Howson, while at the other end a shot-shy Villa side barely threatened.
The best effort they could muster came just after the half-hour mark when Tommy Elphick got on the end of a deep Jordan Ayew free-kick but, at full stretch, lifted his shot just over.
Norwich continued to look the better side after the break, with Robbie Brady stinging Gollini’s palms with a rising drive from a tight angle five minutes in.
Alex Neil’s men were the only side who looked like scoring and should have done just that with an hour on the clock.
A slick move from one side of the pitch to the other ended with Brady having a clear sight of goal but the Republic of Ireland star drilled his shot wastefully wide.
City fans need not have worried, however, as their side took a deserved lead from their very next attack. Oliveira ran to the edge of the box before guiding a low shot towards the bottom corner and an unsighted Gollini stood rooted to the spot as it flew into the back of the net.
Villa’s response to going behind was lacklustre and it was not until the 80th minute that they provided an anxious moment for a well-drilled home side, with a 30-yard free-kick from substitute Ross McCormack drifting just wide.
Jacob Murphy did likewise from open play as Norwich continued to have the better of it and they saw out the game with few alarms.