A brace from Fernando Forestieri and one from George Boyd sealed the contest while the Royals finished with 10 men after having Tyler Blackett sent off.
Wednesday took the lead in the 34th minute after Forestieri received the ball just inside the box and drilled his effort past Vito Mannone via a deflection.
They made it 2-0 in the 54th as Adam Reach shimmied passed two defenders and pulled the ball across to Boyd, who slotted home from close range.
Forestieri added a third in the 71st minute, wriggling his way across the edge of the box and beating Mannone at his near post.
Seconds later, Reading were reduced to 10 men when Blackett, who was on the floor, kicked out at Atdhe Nuhiu and was swiftly given his marching orders.
Luhukay said: “I’m very proud of my team. In this last period, we gathered some important points to stay in the league. We won five out of the last seven games, so the team has its confidence back.
“We have a team that fights for each other. In the first half, we needed a lot of patience to create the chance and sometimes the last ball was not always in the right direction.
“The team had a very good inspiration and motivation to bring a good result to play a good game and bring the support from our fans.
“I think Fernando was very inspirational and very motivating for a good game. He made the important moments, scored goals, he was dangerous and made opportunities for us.
“We are happy for Fernando, but we must also look at what the team has done over the last two months.”
Reading boss Paul Clement said: “First half I though we were okay. I was disappointed to come in a goal down but I thought I saw enough to think we could get back into the game if we improved in a couple of areas.
“I’m really disappointed with the nature of the two goals and our defending in general. For the second and third goals, there were missed tackles in there and that’s not right.
“We’re fighting to stay in this league and that didn’t show me a lot of fight in those two situations. When the third goal goes in it’s game over.”
Commenting on the sending off, Clement added: “It’s right on the far side and all I know is that it was outside of the game. The whistle had gone and it’s not a good situation.
“If it’s for something outside of the game it’s poor and it’s not right.”