The first real chance went to Sunderland with Jules Ahoka timing his run into the box to meet Chris Rigg's cross but directing a header straight at the goalkeeper.
At the other end, Beljo's shot on the turn was heading in before a block from Granit Xhaka deflected it behind.
Sunderland's relief was short-lived as Xhaka could only glance the resulting corner to Stojkovic, who controlled on his chest before thumping home the volley from 15 yards.
Two minutes later, Stojkovic and Beljo combined to set up Mislav Orsic, who skipped past Roefs but had his shot cleared off the line by Thomas Meunier.
Meunier's miscued cross almost crept in for a Sunderland leveller but bounced back off the far post, and a bad night quickly got worse.
The Stojkovic and Beljo link-up brought the second goal for the slick visitors, with the former pouncing on Kevin Danso's poor clearance and chipping a ball through to Beljo, who provided the delicate finish.
Anger was palpable among the home fans and Le Bris' changes at the break suggested he shared their frustration.
Sunderland thought they had the perfect start to the second half when Wilson Isidor headed in a Xhaka free-kick just 71 seconds after the restart, but replays showed he was offside and the goal did not stand.
Chances for Trai Hume, Danso and Brian Brobbey came and went as hopes of a comeback faded.
The ferocity of the booing seemed to subside at full-time, whether as a result of the team's second-half effort or the fact many fans had already left.
Regardless, another poor result leaves Sunderland team devoid of confidence, still seeking the match, or even the moment, that might breathe life into their ailing campaign.