Bruno Guimaraes and Newcastle United are still "dreaming and believing" they can make a late charge into the European places after ending their Premier League losing streak.
Newcastle had lost each of their last four matches in the top-flight, a run which saw them drop down the table to 15th ahead of kick-off, but they got back on track at St. James' Park.
They ran out 3-1 winners over Brighton, with first-half goals from William Osula and Dan Burn putting them in control.
Brighton attempted to force a way back into the match, and halved the deficit through Jack Hinshelwood, but Harvey Barnes' last-gasp strike secured the three points for Newcastle.
Newcastle ended their joint-longest losing run under Eddie Howe in the Premier League, with this their first win by two or more goals since beating Crystal Palace 2-0 in January.
It was a much-improved performance from the Magpies, who recorded a non-penalty expected goals total of 2.1 in the first half. On only seven occasions in the Premier League this season has a side had a higher value in the opening 45 minutes.
Newcastle are now back up to 13th in the table and are only six points behind sixth-placed Brentford with three games left to play, with Guimaraes, who was making his 150th Premier League appearance, still harbouring hopes of finishing the season on a high.
"It felt very good in the changing room before the game. We knew [this game] was important for us, chasing European football for next season," he said. "The points are crucial; we keep dreaming and believing.
"It was a tough game; Brighton are a good team. For everything we have done, we deserve the win.
"They had a lot of chances. In the first half, we were better, but second half, they were better. I am glad we could keep three points.
"We are looking up, not down. We can still play European football next season; we must win the next three games."
As for Brighton, their own European hopes took a blow as they slipped to seventh in the table, with Brentford leapfrogging them after a 3-0 win over West Ham.
Their five-match unbeaten streak was ended in this game, and they conceded at least three goals in a Premier League game for the first time since their 4-3 loss to Aston Villa in December.
Defensive mistakes caused them problems, with goalkeeper Bart Verbruggen at fault for the first goal, getting caught well outside his box – he has made four errors leading to goals in the Premier League this season, more than any other player.
"We dominated the game, except a short period where we conceded two goals and lost a bit of structure," Hurzeler told BBC Sport.
"But the key moments, we were not able to get on our side or manage well, and that's why we lost the game.
"Every time you concede a goal, you can do something better. We knew they'd have a lot of physicality and height, especially at set-pieces.
"The first goal was an unlucky decision [by Verbruggen]. I like players that make decisions; they have a lot of courage. You make mistakes; afterwards, everyone knows better, which is why I prefer players who take responsibility.
"This game didn't go our way, but the only thing we can do is analyse it and bounce back next weekend."