The visitors went closest first as Adam Reach dragging wide, before George Boyd shot over.
At the other end, Jack Stacey's effort was straight at keeper Cameron Dawson, while James Collins dragged wide on the half hour.
The Owls almost had the lead after 36 minutes when Barry Bannan's speculative volley was flicked on to the post by Steven Fletcher.
Elliot Lee drove over for the Hatters, with Dawson saving well from James Justin's 25-yarder.
The visitors went ahead at the start of the second period when Nuhiu's effort was deflected past James Shea from close range.
Luton should have levelled as Justin picked out Luke Berry, who was denied by the legs of Dawson.
Shea did well to prevent Reach making it 2-0, while substitute Dan Potts almost equalised as his left-footer was parried behind by Dawson.
Luton came agonisingly close to levelling with 13 minutes to go, Collins diverting Sonny Bradley's header on to the post with the goal gaping.
Bradley's header was then nodded off the line by Nuhiu as Luton's cup dreams were ended for another season.