Wolves captain Ruben Neves admits only a catastrophe can send them down now.
Toti Gomes’ early header earned a 1-0 win over Aston Villa on Saturday – a fourth straight home victory – and moved Julen Lopetegui’s men onto 40 points.
They are 13th, 10 points clear of the Premier League’s bottom three, and depending on other results could be mathematically safe by Monday night.
It comes after Wolves were bottom at Christmas and Neves knows their job is virtually done.
He told the club’s official site: “It’s not a secret for anyone, with 40 points we are pretty much there. A catastrophe needs to happen. It was really important for us and we can breathe a bit better now.
“It’s a big relief to come out of this fight and to enjoy the three games left in the league. We knew if we won this game, we’d be really close to our goal. It’s really hard to go down on 40 points.
“We had a bad start and changed coach, then the World Cup and we changed coach again.
“A lot of injuries, a lot of players out, but we wanted to achieve our main goal.”
Villa’s European hopes took a hit to keep them eighth and a point behind Brighton, having played three more games.
They host the Seagulls on the final day of the season and also face Tottenham and Liverpool, the other two sides immediately above them before the end of the campaign.
Successive 1-0 defeats could prove fatal in their quest to return to Europe for the first time since 2010-11 and midfielder John McGinn revealed his frustrations.
“We lost a goal from a set-piece, which is never nice, and you give yourselves a tougher task. We created a lot of chances to go and equalise and get more from the game,” he told the club’s official site.
“It’s definitely frustrating. There are a lot of things we could have done better, but overall, we controlled a lot of it.
“We’ve got to be a lot smarter in the final areas with our decision-making like we have been over the last few months.
“As much as when we were winning we weren’t getting carried away, it’s important we don’t let two defeats hamper what could be an exciting end to the season.
“We’ve made it extremely difficult for ourselves now but the challenge is still there for us. We’ll be aiming for three wins in the last three games.”
Silva grateful Fulham's dominance was rewarded with late win
Marco Silva believes Fulham claimed a "deserved win" against Brentford, though admits they should have secured the three points much earlier in their 2-1 victory.
It looked like Vitaly Janelt's 24th-minute strike against the run of play was going to wrap up all three points for Brentford, but Harry Wilson proved the Cottagers' hero off the bench, scoring twice in stoppage time to snatch the three points.
Fulham had dominated from the first whistle and had 26 shots, 12 of which were on target, though they struggled to find a way past their opponents' staunch defence until the 92nd minute.
Wilson became just the sixth player to score an equalising and match-winning goal from the 90th minute onwards in the Premier League, while his second goal was Fulham's latest-ever Premier League winner at 96:46.
Silva was delighted with how his team pushed until the final seconds to ensure they came away with a win.
"It was definitely a deserved win. We started on the front foot and dominated all the game. In the first 20 minutes, we had two clear chances to score," Silva told BBC Sport.
"After they scored, we didn't lose the confidence and the trust in ourselves, we kept pushing them back, and we created enough to not be losing at half-time.
"I told the players this is football, it can happen, but we have to keep pushing, working hard and playing our way.
"It was late, it should've been much before, but that's football."
Brentford, meanwhile, have now dropped a league-high 14 points from winning positions in the Premier League as they suffered a fifth consecutive away defeat in the competition.
In fact, they are the first side in the competition's history to score the first goal in four consecutive away games and lose all four.
They had defended resolutely until their late lapse in concentration, and even had a chance to win it, only for Bernd Leno's impressive save to keep out Fabio Carvalho in the 95th minute.
Thomas Frank, though, admitted he was not yet ready to take the positives from the performance after the disappointment of their late defeat.
"It was tough. It is emotionally very tough right now," Frank told Sky Sports.
"When you are leading in the 92nd minute, and you lose, it is tough. I don't think we hit our highest level. I think on the day Fulham were better.
"There was a lot of good defending and effort, and I thought that would have given us the win. We could have won it with the chance for Fabio Carvalho and then we lost.
"When we look at the game back, and we are more cool-headed, we will probably be very happy with the defensive standard. I thought there were unbelievable blocks, and recovery runs and all that we did well. On the ball, we didn't do enough."
Fulham 2-1 Brentford: Wilson's late brace seals comeback win
Harry Wilson scored twice in stoppage time as Fulham came back to beat Brentford 2-1 in an enthralling West London derby.
Wilson was the hero from Fulham's bench on Monday, as Marco Silva's team – who were on the wrong end of a late comeback against Everton last time out in the Premier League – salvaged a victory from the jaws of defeat.
Fulham will feel it was a win they earned from a match they dominated from the off, with the Bees having taken the lead against the run of play through Vitaly Janelt's stunning 24th-minute strike.
But the Fulham pressure finally told when Wilson rose high to flick in his first in the 92nd minute, and – after Bernd Leno made a superb stop to thwart Brentford at the other end – the former Liverpool midfielder nodded in again to send Craven Cottage into raptures.
Fulham's win takes them up into ninth, while Brentford drop to 12th after suffering a fifth league loss of the season.
Data Debrief: Super-sub Wilson to the rescue
Fulham will feel they deserved to come away from that match with three points, having had 26 shots, 12 of which were on target, in an incredibly dominant display.
They also had 46 touches in the opposition box compared to Brentford's nine, but they could not make those count, at least until Wilson's late intervention as he finally broke through Brentford's stubborn defence.
The Welshman scored with both of his shots on target, having three attempts overall, with his goals coming from a combined 0.19 expected goals.
The Bees looked sure to get a first away win, and first clean sheet, of the Premier League season until their late lapse in concentration, and they have now dropped 14 points from winning positions in the competition this season, more than any other team.
Arsenal sporting director Edu steps down
Arsenal have confirmed Edu has resigned from his role as the club's sporting director.
Edu, a former Arsenal player who was part of the "Invincibles" squad in the 2003-04 season, has been involved in the behind-the-scenes running of the Gunners since July 2019.
He first returned to the club as technical director, and was promoted to sporting director in November 2022.
Edu has played a key role in supporting Mikel Arteta, and helping the Spaniard transform the Gunners into Premier League title contenders.
Reports emerged on Monday, however, that the Brazilian was quitting his role, with speculation mounting that he will be joining Evangelos Marinakis' footballing organisation - the Greek magnate owns Nottingham Forest and Olympiakos.
"This was an incredibly hard decision to make," Edu said in a statement released on Arsenal's website.
"Arsenal has given me the opportunity to work with so many amazing people and the chance to be a part of something so special in the club’s history. It has been a special journey.
"I've loved working with so many great colleagues across our men’s, women’s and academy teams, especially Mikel, who has become a great friend.
"Now it is time to pursue a different challenge. Arsenal will always remain in my heart. I wish the club and its supporters only good things and all the very best."
The news comes after Arsenal were beaten 1-0 by Newcastle United on Saturday to leave them seven points adrift of Premier League leaders Liverpool.
Arsenal face Inter in the Champions League on Wednesday.
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