It was the second game in charge for new manager Darren Moore who arrived at Hillsborough after leaving League One side Doncaster on Monday.
The Royals went in front in the 29th minute after defender Julian Borner had been sent off for bringing down George Puscas, with Michael Olise slamming in the resultant penalty.
Reading dominated their 10-man opponents thereafter, with second-half goals from Lucas Joao and Andy Yiadom settling the game.
“For the first half-hour before the sending-off I thought that we carried quite a good threat going forward,” said Moore. “But that red card gave Reading a bit of momentum. Even so, I thought we did well up until half-time with 10 men.
“It was imperative that we kept it tight in the second half, but just at a crucial time they scored their second goal. From then on, the game got away from us.
“I’ve not really looked back at the red card yet. But in real time, it looked like a mis-control of the ball and then Puscas got the run.
“I’ll wait until I see it back again before speaking to Julian.
“The game’s gone now, we can’t cry over spilt milk. I’ve just got to look ahead and we’ve got more important games coming up.
“I’ve only just arrived here, it’s a big learning curve for me at the moment.
“We now have to focus in going forward and we just have to dust ourselves down. It’s been such a busy week, a lot has happened.
“It’s essential that we all stick together. That’s got to be the main focus.
“All the odds look to be stacked against us (in the relegation battle) but we’re still in there with a fighting chance and we have to keep our belief.
“There’s been a lot going on at the club this week, but one thing that I’ve seen is that we have a great desire to do well in this group.”
Reading manager Veljko Paunovic admitted his side’s win helped ease the pain of a shoulder injury he sustained when taking part in a training session in midweek.
Paunovic had his left arm in a sling during the game, and he said following a third successive victory: “The most important thing was that the team did well today and I’m very happy about that.
“I got the injury in one of our recovery sessions in training. It was pretty nasty, it was the ligaments, but I feel okay now and, of course, the victory helps that. All of it helps.”
Reading: Rafael Cabral, Yiadom (Tomas Esteves 90), Holmes, Moore, Richards, McIntyre, Semedo, Laurent (Azeez 90), Olise (Tetek 82), Puscas (Baldock 83), Lucas Joao (Aluko 67). Unused substitutes: Southwood, East, Dorsett, Camara.
Sheffield Wednesday: Wildsmith, Urhoghide, Lees, Borner, Palmer, Harris (Marriott 70), Hutchinson, Shaw, Windass (Pelupessy 85), Bannan (Penney 32), Paterson (Rhodes 70). Unused substitutes: Reach, Dunkley, Brown, Jackson, Kachunga.
Referee: J Linington (Isle of Wight).