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Sidwell strode forward to drive home from 20 yards with just two minutes left, just reward for a second-half onslaught from the home side.
Victory left Reading still in with a chance of sneaking into the top six, though Steve Coppell's side will need three separate results to go their way even if they win at Watford on the final day of the season.
West Brom, whose Premiership return was already secured before this game, also need a minor miracle to snatch the First Division title from Norwich, who now lead the division by five points with two games left.
Yet for most of this match, Gary Megson's Baggies seemed content to settle for promotion and hand the title to Norwich.
The visitors lacked ambition against a Reading side frantically searching for the win that would prolong their season.
Neither side seriously threatened in a first half bereft of clear-cut chances, but Reading stepped up a gear after the break.
Young striker Dave Kitson almost put them in front three minutes into the second half, sprinting on to Sidwell's pass and cracking a low shot which Russell Hoult did well to turn round a post.
Four minutes later, Kitson wasted a glorious chance to break the deadlock when he headed over the crossbar from substitute Dean Gordon's pinpoint cross.
And the lanky striker made it a hat-trick of missed chances when he sidefooted over from a low Paul Brooker centre eight minutes from time.
With Reading fans staging "Ginger Day" in honour of Kitson and fellow red-head Sidwell, it seemed as though the theme may have been poorly timed.
But Sidwell ensured the Ginger party started in earnest when he raced clear two minutes from time then, with West Brom's defence backing off at pace, cracked a low shot into the bottom left-hand corner of Hoult's goal.
Lloyd Dyer had earlier put West Brom's best chance into the side-netting and a frantic late response left Reading nervously hanging on, but Steve Coppell's men deservedly survived to take their play-off chase to the last game of the season.