Tottenham remain in the Premier League relegation zone after Georginio Rutter's stoppage-time equaliser salvaged a 2-2 draw for Brighton, while Leeds beat Wolves 3-0 on Saturday to pull clear of the bottom three.
Spurs were headed for their first win in 15 league games as they twice led in Roberto De Zerbi's first home match in charge.
Pedro Porro's header was quickly cancelled out by Kaoru Mitoma's spectacular volley in first-half stoppage time.
Xavi Simons' stunning strike 13 minutes from time sparked an outpouring of joy around the state-of-the-art Tottenham Hotspur Stadium.
Yet, the home fans were stunned five minutes into time added on when Jan Paul van Hecke outmuscled Kevin Danso and squared for Rutter to blast high into the net.
Spurs, who have not played outside the top flight in nearly 50 years, edge to within one point of West Ham in the battle for survival.
But the Hammers have a game in hand and could stretch that advantage when they travel to Crystal Palace on Monday.
Brighton's equaliser also saved Wolves from being officially relegated.
But their eight-year stay in the top flight is coming to an end as Leeds opened up an eight-point cushion on the bottom three.
Fresh from a first league win away at fierce rivals Manchester United since 1981, Leeds all but secured their top-flight status.
Two goals in two first-half minutes from James Justin and Noah Okafor put the home side in control before Dominic Calvert-Lewin's penalty in stoppage time rounded off the scoring.
Tottenham's woeful campaign has been compounded by an impressive return to the top flight by Sunderland and Leeds, to buck the trend of recent seasons.
For the past two years all three promoted sides have gone straight back down.
However, Daniel Farke's men not only look set for survival, but could reach a first FA Cup final since 1973 should they beat Chelsea in next weekend's semifinals.
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HOWE UNDER PRESSURE
Bournemouth piled more pressure on Newcastle manager Eddie Howe with a 2-1 win at St James' Park.
The Cherries showed no ill effects from the news that Andoni Iraola will depart as boss at the end of the season.
Marcus Tavernier and Adrien Truffert struck for the visitors to extend their unbeaten Premier League run to 13 matches.
Bournemouth climb to eighth and within four points of the Champions League places.
Newcastle, by contrast, remain in 14th with their hopes of European football next season all but over.
Despite delivering Newcastle's first domestic trophy for 70 years last season, Howe is another high-profile Premier League manager who could move on at the end of the campaign.
Brentford missed the chance to leapfrog Chelsea into the top six after being held to a 0-0 draw by west London rivals Fulham.
Chelsea need to snap a three-game losing streak to revitalise their chances of Champions League football next season when Manchester United visit Stamford Bridge in a 1900GMT kick-off.
Third-placed United lead the Blues by seven points but travel to London decimated by injuries in defence.
Leaders Arsenal travel to Manchester City in a clash that could decide the destiny of the title race on Sunday.
The Gunners hold a six-point lead, but City have a game in hand and home advantage when the top two clash at the Etihad Stadium.