Wales international goalkeeper Hennessey, back in the team after serving a one-match ban, punched the ball into his own net after just four minutes.
Wolves had made their best start to a season since 1949 by following an opening day draw with seven straight wins, but they couldn't bounce back from Hennessey's error as Mick McCarthy's side failed to score for the first time this season in the league.
Their fate was confirmed in the 71st minute when the impressive Andre Bikey doubled Reading's advantage.
Substitute Kalifa Cisse then sealed the win two minutes from time to earn Steve Coppell's in-form team their fourth win in the last six Championship games.
Hennessey quickly handed Reading the initiative when he failed to deal with an inswinging right-wing corner from Stephen Hunt.
Hennessey was under pressure at his near post but in attempting to make a punched clearance, all he succeeded in doing was turning the ball into the net.
It completely knocked Wolves out of the confident stride they had shown previously this season and they struggled to find a way through a Reading defence that was superbly marshalled by Bikey.
They were fortunate not to fall further behind in the 32nd minute when Stephen Hunt whipped in a right-wing centre and his younger brother Noel headed the ball goalwards, only for the well-placed Kevin Foley to clear off the line.
Ironically, after that lucky escape, Wolves surged straight upfield to create their best chance of the game.
David Jones fed Andy Keogh and the Irishman only had Marcus Hahnemann to beat, but the American did well to dive low to his left to smother the ball.
It was a costly miss by Keogh and was the last time Wolves seriously threatened.
Reading were unlucky not to move further ahead in the 56th minute when Jimmy Kebe hit the post and Ivar Ingimarsson was denied by a smart save by Hennessey following another Stephen Hunt corner.
Kebe may have failed to score himself but he did create the clincher for Bikey.
His right-wing cross left the Wolves defence flat-footed and Bikey planted a firm close-range header past Hennessey from four yards.
Substitute Cisse then made the final scoreline even more emphatic in the 88th minute, when he latched on to an excellent through ball from Shane Long to steer a low drive under the advancing Hennessey.