Sidwell, 22 on Sunday, was made skipper in the absence of injured Graeme Murty and rewarded manager Steve Coppell's faith with a match-winning performance.
Ivar Ingimarsson scored late on to seal it for Reading who had lost six and drawn two of their previous eight meetings with The Foxes.
City almost went ahead at the end of an evenly fought first half when Nathan Blake struck a post and Lilian Nalis had a shot scrambled off the line, but they were the only clear chances they created in an otherwise lifeless performance.
There were few chances in the first half, but Reading were almost gifted the lead through a blunder by Dion Dublin whose weak header back to his keeper was seized on by David Kitson who looked likely to score until a late intervention by Nikos Dabizas.
At the end of the first half Blake headed a Keith Gillespie cross against the post and Andy Hughes denied Nalis with a goalline clearance, but City were never to go so close again.
After the restart, Stuart Taylor came to Leicester's rescue with a great save to keep out James Harper's driven free-kick and then performed acrobatics to prevent City's debutant defender Richard Stearman from putting through his own net.
But there was little he could do about Reading's first goal on 68 minutes.
Gillespie was harshly ruled to have fouled Glen Little halfway between the penalty area and the touchline.
Little's free-kick found Sidwell lurking 20 yards away from goal and before the City defence could react, he drove a rising thunderbolt into the top left-hand corner of Taylor's goal.
Then Reading sealed up the points on 82 minutes when Nicky Shorey swung over a corner and Ingimarsson rose unchallenged to glance a header beyond Taylor's reach.