Crystal Palace's victory at Newcastle means they have amassed enough points to avoid the drop, according to manager Roy Hodgson.
The Eagles' victory saw them take their points tally to 39 - 11 clear of 18th-placed Cardiff with just five games left to play.
Palace skipper Luka Milivojevic scored the decisive goal at St James' Park as the fired home from the spot after Wilfried Zaha had been felled in the penalty box by DeAndre Yedlin late on.
"I think 39 points, with our goal difference, will see us over the line," Hodgson told Premier League Productions.
"It was a very hard-fought game and I'm pleased with the way we handled it. I am very, very proud of the team's performance."
Both sides had seen goals disallowed in the first half; Salomon Rondon was called offside after bundling home Matt Ritchie's knockdown before James Tomkins fired in from a corner only for the flag to be raised due to James McArthur's offside position.
The hosts then lost Florian Lejeune midway through the second period as he was carried off on a stretcher after suffering a nasty knee injury.
The victory lifts Palace to 12th while the Magpies drop to 15th, though they are still seven points clear of Cardiff, who currently occupy the final spot in the relegation zone.
Had Palace beaten Watford last month they would have had an FA Cup semi-final at Wembley to look forward to this weekend. Instead, it was a trip to St James' Park in the Premier League.
The hosts dominated for much of the first period and Eagles keeper Vicente Guaita was called into action on a number of occasions to deny Rondon.
Palace, however, held firm and looked dangerous on the break.
And it was from a lightning counter-attack with which they found the winner as Zaha skipped past Fabian Schar before being fouled by Yedlin. The skipper did the rest from the spot.
Milivojevic has now scored 11 goals across all competitions this season and, incredibly, 10 of those have come from the spot.
Palace have had more penalties awarded than any other club in the Premier League this season.