Oliveira scored the only goal of the game with an excellent long ranger in the 31st minute as the hosts, who were parked in the relegation zone not too long ago, continued their recent resurgence.
The win eased Salgaocar's relegation worries as they climbed two places to the sixth spot on the nine-team league table. The former champions are on 12 points from an equal number of matches.
Shillong meanwhile, dropped one place to seventh with nine points from 11 matches.
The hosts were off to a bright start and created a host of chances in the early stages. They had their first opportunity in the fourth minute when Penn Orji received a pass from Samuel Lalmuanpuia and managed to turn and shoot from inside the box. But his attempt went wide of the far post.
Calvin Mbarga missed a sitter for Salgaocar in the 18th minute after Jackichand Singh had taken the ball off Shillong's Samuel Shadap and crossed into the box. But Mbarga headed it wide from close range.
Alesh Sawant then saw his effort brush off Konsham and go wide just five minutes later, although the referee awarded a goal-kick.
The hosts took the lead in the 31st minute as Konsham headed away Brian Mascarenhas' corner-kick but only as far as Oliveira. The Salgaocar midfielder took the shot on the bounce and found the back of the net from around 20 yards.
It could well have been two goals in two minutes for Salgaocar as Mbarga set up Jackichand in the 33rd minute, but the winger's shot from the edge of the area went wide.
Salgaocar had their chances in the second half as well, but were let down by poor finishing. The visitors also wasted a couple of chances that came their way and could not capitalise on their opponents' wastefulness.Published 12 Mar 2016, 20:12 IST