Portugal international Oliveira's goal on the hour stretched Nottingham Forest's run of Championship games without defeat to 13 matches.
Leeds were well below their best as their sequence of six unbeaten home matches came to an end but Forest confidently bounced back from their FA Cup defeat against Watford last weekend.
Souleymane Doukara, a scorer in four of his previous six games, almost added to his tally with just three minutes gone, heading narrowly wide as he met a right wing cross from Stuart Dallas 12 yards out.
Yet such moments were all too rare from Leeds who found it hard to break down Forest for most of the proceedings.
Supporters of two clubs eager to recapture past glories rolled back the years by chanting the names of legendary managers Don Revie and Brian Clough
And the crowd held its breath as Gary Gardner rattled the Leeds bar in the 20th minute.
Gardner was fouled 25 yards out and when Leeds could only clear Jamie Ward's free-kick to the loanee from Aston Villa, he unleashed a power-packed shot which struck the bar with keeper Marco Silvestri diving full length to his left.
Forest went close again six minutes later when Ben Osborn's long range drive deflected off Giuseppe Bellusci to Robert Tesche who volleyed high and wide from eight yards.
Dougie Freedman's men had created the better chances and defender Eric Lichaj, whose loan spell from Aston Villa to Leeds was cut short by a knee injury in 2011, broke free down the right, only to fire wide of the near post.
Leeds needed to be much more creative in the second half after failing to test Forest keeper Dorus De Vries in the opening 45 minutes but it took a defender to test the away keeper seriously for the first time
With the second half a mere two minutes old, Scott Wootton tried his luck with a 20 yard shot which De Vries saved low down.
Winger Dallas then blazed wide when well placed but Silvestri was soon back in action at the other end, getting his body behind a speculative effort from the lively Ward.
Forest were finally rewarded when Lichaj sent over a measured cross from the right and number 17 Oliveira's close-in header grazed the far post on its way into the net.
Leeds withdrew Dallas, Toumani Diagouraga and Wootton, replacing them with Mustapha Carayol, Lee Irwin and Tom Adeyemi, while Forest sent on Oliver Burke in place of Ward and Dexter Blackstock for Oliveira, but there was little change in the pattern of play, with Forest continuing to hold on to their slender lead.
Carayol impressed with his cameo appearance but the three crosses he managed found nobody in the box to finish them off with Chris Wood sat watching in the stands still out injured.
Source : PA