Chadwick, a late replacement for fellow goalscorer Micky Evans, struck with virtually his first touch - sticking out a leg to divert Paul Wotton's low free-kick across goal and beyond the reach of goalkeeper Marcus Hahnemann.
The dramatic finale rocked Reading, who had battled back from the setback of an Evans opener to equalise through record signing Leroy Lita.
Evans broke the deadlock midway through the first half, sliding in to turn home Rufus Brevett's low cross after Reading had failed to deal with a training ground throw-in routine from the visitors.
The Royals barely threatened a comeback in a lacklustre first half and, with wide men Glen Little and Bobby Convey struggling to find their range, the home side lacked a cutting edge.
That changed in the second half though, with the ammunition from the Reading wide boys a crucial factor in the home side's change of fortune.
Little's dazzling run from his own half ended with a pass that Kevin Doyle latched on to but blazed wide, from Reading's first real attack of the game seven minutes into the second half.
And, just two minutes later, Reading were level as Lita thumped home a header from Graeme Murty's cross after Convey had won and then quickly taken a free-kick wide on the right.
Lita then saw a deflected shot scrambled away from goal by defender Hasney Aljofree after a neat Reading build up saw Steve Sidwell tee up the lively striker.
Defender Ibrahim Sonko sliced a shot way off target and then failed to find the net with a header from four yards as Reading pushed for a winner, switching to 4-3-3 with the introduction of last season's top scorer Dave Kitson for the final 15 minutes.
But it was Bobby Williamson's late substitution that won the day.
Former Everton striker Chadwick was felled out wide by Ivar Ingimarsson and was then on hand to turn the ball home from captain Wotton's free-kick.