The Royals, who had lost their previous four matches, looked to be heading for another defeat when Robbie Keane fired Spurs ahead from the penalty spot, but the home side came back strongly and eventually ran out easy winners as the Tottenham defence collapsed dramatically.
Shorey got Reading level with a long-range left-footer before Sidwell bundled them in front on the stroke of half-time.
Seconds after sub Jermain Defoe had wasted a glorious second-half chance to level, Kevin Doyle made victory safe for the home side.
With lively winger Ki-Hyeon Seol pushed into a central striking role alongside top scorer Doyle, Reading were full of early running.
Sidwell had the game's first chance, created by some neat play on the left by Seol and Stephen Hunt, but skied his shot from the edge of the box.
But Spurs, unbeaten in their previous five Premiership matches, looked dangerous when they suddenly got out of first gear midway through the opening half.
Hossam Ghaly did well to cut the ball back from a tight angle to tee up the dangerous Dimitar Berbatov, and only a superb saving tackle from Reading captain Graeme Murty denied the striker a clear shot at goal.
Reading were welcoming back Murty after his four-game injury absence had coincided with their losing streak, and the former York City star seemed to give his side a real lift.
But it was Spurs that broke the deadlock on 24 minutes. Ghaly's fast feet were too quick for Ibrahima Sonko, who tripped the midfielder as he ran on to Keane's throughball, giving the Republic of Ireland international the chance to fire home from the spot.
It was tough luck on a Reading team that had been lively up to that point, but Steve Coppell's side responded well.
Shorey hauled them level on 38 minutes with a real bolt from the blue, stepping on to Glen Little's cross-field pass and, as Michael Dawson backed off, letting fly with a left-foot shot that screamed past England keeper Paul Robinson.
Robinson was beaten again seconds before half-time when Spurs were slow to organise defensively for a Reading corner, leaving Doyle completely unmarked.
The striker failed to connect with Little's corner but, as the ball floated past him, Sidwell was the first to react and bundled the ball into the roof of the net.
Sleepy Spurs threw on Defoe and two-goal Carling Cup hero Tom Huddlestone in a bid to spark a revival but it was Reading that threatened more.
The impressive Sidwell teed-up Doyle for a left-foot shot on the turn that Robinson batted away, but the crucial turning point came 10 minutes from time.
Ghaly played Defoe in behind Ivar Ingimarsson only for the England striker to pull his shot into the side-netting when he looked odds-on to score.
Immediately, from Marcus Hahnemann's resulting goal kick, Reading sub Leroy Lita flicked a header into the path of Doyle, who thumped a left-foot shot past Robinson to seal a deserved victory for the home side.
Reading's welcome return to form was witnessed by a crowd of 24,110, a record attendance for the Madejski Stadium.