Vuckic entered the fray as a 10th-minute substitute after Ryan Taylor had injured his right knee by landing awkwardly.
It took the 20-year-old Slovenia international just 11 minutes to make an impact, as he collected a quick throw-in from Danny Simpson on the right, before cutting inside and finding the net with a deflected volley from 25 yards.
With most people expecting to see a penalty kick awarded and a red card shown to the Dutchman, referee Stephan Studer shocked everyone by booking Chumbinho for simulation.
Alan Pardew's men had dominated the first half but they had to endure a nervous final 45 minutes, as Atromitos poured forward in search of an equaliser that would have forced extra time.
Chumbinho had a goal correctly ruled out for offside and Walter Iglesias went excruciatingly close with a low drive late on.