The striker, capped 16 times by Portugal, set the Canaries on their way shortly after half-time before Harrison Reed wrapped up all three points with a superb strike late in proceedings.
Without a win in their opening two matches, Norwich had to wait until after half-time for a morale-boosting opener, with Oliveira seizing on Mario Vrancic's smart pass.
New boss Daniel Farke suffered defeat against Sunderland in his first home league match in charge but Reed, on loan from Southampton, sealed the host's first victory of the campaign by picking out the top right corner in the 82nd minute.
The result lifts Norwich to 10th place, ahead of QPR on goal difference as Ian Holloway's men miss a chance to move into the top four.
Meanwhile, Sunderland maintained its unbeaten run despite letting an early lead slip in a 1-1 draw with Sheffield Wednesday at Hillsborough.
Simon Grayson's side looked on course for a second straight away victory until David Jones thumped a stunning 25-yard equaliser past Jason Steele.
Jones' goal secured the Owls just their second point of a slow opening to the season, a start made worse when George Honeyman fired the visitor ahead inside five minutes.
Sunderland had chances to put the result beyond doubt but were made to pay with 20 minutes remaining, and it could have been worse had Gary Hooper not hit the bar with a late half-volley.
The Black Cats' next assignment is at home to Leeds United on Sunday (AEST), while Wednesday continues its search for a first victory at fellow promotion hopeful Fulham.