Austrian striker Nuhiu, who scored twice at the Riverside earlier in the season and the winner in the home game against Boro last year, converted a 52nd-minute penalty to open the scoring.
On-loan Manchester United striker Keane headed in the second three minutes later to seal the points and inflict a second defeat in three games on Wednesday’s high-flying opponents.
Boro winger Albert Adomah went down in the 18-yard box under Jacques Maghoma’s challenge in the third minute but his penalty appeals were waved away by referee Stephen Martin.
Maghoma then saw his partially-blocked shot from 15 yards claimed by visiting goalkeeper Dimi Konstantopoulos with Keane waiting to pounce.
The home side were edging a scrappy opening period and Liam Palmer sent a speculative left-foot shot wide before Keane headed narrowly over from close range following a flick-on by strike partner Nuhiu.
Midfielder Adam Clayton was way off target with a long-range drive at the other end before Boro’s Adam Forshaw lobbed the ball over advancing Owls keeper Keiren Westwood, only to see his effort land wide of the left post with Kamil Zayatte ready to clear.
Owls left-back Claude Dielna tested Konstantopoulos in first-half injury time, smashing a left-footed volley from the edge of the box which flew towards goal but was too close to the Greek keeper’s body.
Boro striker Patrick Bamford wriggled free on the right early in the second half but his centre was too strong from Clayton before Wednesday took control of the game with two goals in three minutes.
Former Austria Under-21 international Nuhiu found the bottom left corner from the spot in the 52nd minute after Kenneth Omeruo was adjudged to have handled while challenging Keane.
Keane then grabbed his goal, bravely stooping to nod into the roof of the net from close range after Nuhiu’s flicked header from Lewis McGugan’s free-kick hit the right post and bounced across the six-yard box.
McGugan slipped Keane through on goal nine minutes later but the forward’s right-footed shot was straight at Konstantopoulos before Bamford, on loan from Chelsea, saw a header saved by Westwood.
Wednesday right-back Palmer produced a goal-saving challenge with 11 minutes remaining, sliding in to deny Kike a tap-in after the Spanish striker had been teed up by Bamford.
Kike threatened again in stoppage time but it was Wednesday’s day as they held firm to do the double over their promotion-chasing opponents and record their first home win since Boxing Day.