Michail Antonio and Connor Wickham were also on-target for the Owls, while Reading defender Sean Morrison scored an own goal as Sky Bet Championship strugglers Wednesday claimed their first three-point haul of the campaign.
There were consolation goals from Pavel Pogrebnyak and Adam Le Fondre, who netted from the penalty spot, on a disappointing day for the Royals.
Wednesday went ahead on 18 minutes after a long ball from Kamil Zayatte was misjudged by left-back Stephen Kelly which allowed Antonio in behind.
The Owls winger lured the onrushing Alex McCarthy wide before laying the ball back to Fryatt to score his third goal of the season.
The hosts then went two goals to the good just six minutes later with Antonio receiving the ball from Seyi Olofinjana on the right, before cutting inside and curling into the bottom left hand corner from just outside the area.
The momentum was with Wednesday and they had a chance a minute later to increase their lead even further with Fryatt put through, but while his effort beat McCarthy it was pulled wide and too quick for an on-rushing Antonio to grab a decisive touch.
Reading then cut the deficit on 34 minutes as Chris Gunter's cross was met by Pogrebnyak, who steered an excellent header past Chris Kirkland.
Wednesday restored their two-goal advantage on 42 minutes when Olofinjana won the ball from Danny Guthrie before playing in Wickham.
The 20-year-old, who earlier this week linked up with the Owls for a second loan spell from Sunderland, saw his shot saved by McCarthy but the ball rebounded off Morrison and slowly crawled into the open goal.
After half-time, the Royals came out all guns blazing, with Guthrie firing wide from 25 yards, while Hal Robson-Kanu spooned over the bar from a decent position.
Dave Jones' men then put themselves three goals to the good on 56 minutes.
Antonio beat his man down the right side and drilled a cross to to Wickham, who blasted the ball into the roof of the net.
It was five just after the hour mark, with Wickham and Fryatt combining before the latter raced through on goal and lifted the ball over an onrushing McCarthy.
Reading managed a consolation goal just before the end as Pogrebnyak was brought down in the box by Reda Johnson, with substitute Le Fondre placing his penalty past Kirkland.
The win lifts Wednesday out of the drop zone on goal difference, while Reading drop to sixth.