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The England Under-21 midfielder blasted his seventh goal of the season with two minutes left, just as it seemed Watford would frustrate Steve Coppell's side.
Hornets captain Neil Cox had gifted Reading a breakthrough on 59 minutes when he headed past his own keeper, Lenny Pidgeley.
The visitors were level within seconds when substitute Lee Cook spectacularly finished off a Paul Devlin cross.
But Pidgeley was beaten again in the closing stages when Sidwell's shot deflected past him into the roof of the net.
It was hard luck on the young keeper, on loan from Chelsea, who had performed heroics to keep Reading - and his own team-mates - out for long period.
The keeper was called into action within two minutes, forced to push away a misdirected header from one of his team-mates as Neil Ardley flicked on a corner from Andy Hughes.
And the young keeper produced an even better save on 34 minutes when he dived low to his right to push a 25-yard effort from Nicky Forster round a post.
And when Pidgeley was finally beaten, it was by his captain, Neil Cox.
The centre back turned from hero to villain as he headed into his own net just seconds after denying Forster a certain goal.
Hughes' throughball set Forster up for a clear shot at goal, but Cox tracked back superbly to block the effort.
But when Hughes played another throughball just seconds later, Forster's pressure forced Cox into a header which sailed past his own keeper.
Reading's apparent breakthrough lasted less than a minute as Watford levelled through substitute Cook.
Devlin appeared to handle in the build-up, but there was nothing wrong with his far-post cross which eluded goalkeeper Marcus Hahnemann and gave the lively Cook the chance to rifle home a spectacular finish.
Incredibly, Reading were nearly gifted another own goal by Cox in the closing minutes, but this time his deflection from a Graeme Murty shot flew into the side netting.
And it was left to Sidwell to secure victory for the home side, their seventh in 11 games under Coppell.