The Owls broke the deadlock when Oxford failed to clear effectively and Nuhiu headed home from close range.
They nearly doubled the lead when Marco Matias reached Modou Sougou's cross but keeper Sam Slocombe saved his header.
Alex MacDonald almost found Oxford a late equaliser but his free-kick went just over the crossbar.
Atdhe Nuhiu's second-half goal helped Sheffield Wednesday overcome League Two side Oxford United to seal their place in the Capital One Cup third round.