Keane, centre, celebrates his match-winning strike at Reading
Robbie Keane scored the game's only goal as Tottenham's first win in six plunged Reading into the drop zone and in stark danger of relegation.
The Irishman clipped in after good work from Darren Bent, who himself twice went close as Spurs dominated early on.
Reading finally found their feet in the second half and Dave Kitson and Liam Rosenior both forced fabulous saves from Radek Cerny in a tense finale.
But Bent also hit the post for Spurs and the visitors found no way through.
It means the Royals must now get a result against Derby on the last day of the season and hope that Fulham drop points.
However, they may have to sharpen their skills in front of goal as their failure to break down a resolute Spurs defence extended their barren spell in front of goal to six matches and more than 550 minutes.
It has been a steady slide down the Premier League table for the Royals, who came into the match on a run of just three wins since Christmas and against an opposition who had scored nine goals in three games against them this season.
Coppell admitted his team were second best
They might have received a fillip before the game when Dimitar Berbatov's name was not on the Spurs team-sheet because of a groin injury, but it is hard to imagine the Bulgarian tormenting the home defence much more than Keane and Bent did in an utterly one-sided first half.
Bent, in just his 11th start of the season, was full of running and he got the first chance of the match when he dashed behind the Reading defence to force a good stop with his feet from home keeper Marcus Hahnemann.
Keane says his team's performance over the season has 'not been good enough'
Keane, alongside the impressive Steed Malbranque, was allowed the freedom of the Madejski Stadium as Spurs dominated possession, and it was the Irishman who broke the deadlock on 16 minutes, dancing past a couple of defenders in the box following Bent's driving run before clipping into the corner superbly.
Any hope the goal might wake the hosts from their slumber was extinguished with Spurs comfortable and, after Keane's free-kick had been palmed away, Malbranque clipped in what would have been a brilliant second but for an incorrect offside call from the officials.
Leroy Lita and Kevin Doyle did their best to ensure Spurs' defenders were kept on their toes at the other end, but found Jonathan Woodgate and Michael Dawson in unrelenting mood.
And only a desperate saving tackle from Liam Rosenior on Keane in the box kept the score to 1-0 as Reading trudged off at half-time punch-drunk.
Something had to change at the break for the hosts but for the first five minutes of the second half, Spurs picked up where they left off - Malbranque prodding wide on the stretch five yards out from Keane's cross-shot and Bent denied seven yards out by Nicky Shorey's fabulous block.
However, as news of relegation rivals Fulham's lead against Birmingham filtered into the ground, Reading suddenly found their feet.
Poyet was pleased with the clean sheet
Lita was at the heart of the hosts' good play in a spell that had Spurs reeling a little, and Andre Bikey almost snatched an equaliser when his 20-yard drive was deflected over his own bar by Didier Zokora.
At just 1-0 up, as has so often been the case of late, Spurs looked vulnerable, and substitute Marek Matejovsky might have done better when his shot from the edge of the area drifted wide of Radek Cerny's goal.
With time running down the match was truly end to end, Reading finally full of puff and Spurs looking to score on the counter - something they almost pulled off when Bent broke and smashed a drive on to the bottom of the post late in the game.
Still, there was time for Reading to salvage something and only Cerny in the Spurs goal prevented them doing so, the Czech brilliantly stopping Kitson's near-post shot from eight yards before pulling off an even better stop from Rosenior's 20-yard drive.
It was as close as Reading got in the end, Tottenham's first clean sheet in nearly two months and only their third away win all season ensuring the Royals must endure the final day of the campaign relying on other results to go their way.
Reading manager Steve Coppell: "Tottenham were unbelievable and we found it almost impossible to contain them. They've massively under-achieved this season in the league, and we struggled to match their quality.
"We've been fully aware all season of the trouble we could be - and now are - in, but there's no point looking back. We know what we've got to do next week now - we have to win.
"We've got the stomach for the fight, no question, but we need to win. We might be lacking in confidence and a bit of belief right now, but we will prepare ourselves for a final day of enormous proportions."
Tottenham first-team coach Gus Poyet: "I think we played a great game. It was always going to be difficult because of what Reading are playing for, but I'm very pleased with our performance.
"We kept the ball well, created chances and kept a clean sheet. We totally deserved the win, although it's obviously frustrating when you dominate a match so much and only score one goal.
"There's one week to go of the season now and the first thing we have to do is win against Liverpool next week. Then comes the other side of the job - the phone calls, the meetings and making sure we are all totally prepared for the challenges of next season."
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