The Black Cats will be guaranteed another season of Barclays Premier League football if they beat West Brom at the Stadium of Light on Wednesday evening, and even a point is likely to be enough to keep them up regardless of what Norwich do against Arsenal on Sunday because of their superior goal difference.
For head coach Poyet, who took over in October last year with his side having collected just a single point from their opening seven league fixtures, that would represent a major achievement.
Asked if it would feel like winning something, the 46-year-old Uruguayan said: "Nearly, yes, it's a good shout
Probably.
"Normally you don't celebrate when you finish 16th or 15th in the league
We will
It's true, we will."
Sunderland, of course, came within 35 minutes of genuine glory on March 2 when they led Manchester City 1-0 in the Capital One Cup final at Wembley before eventually going down 3-1.
However, their next six league games yielded just one draw and as they slipped seven points adrift of safety, they looked to be destined for the Sky Bet Championship until they embarked upon an unlikely run of results.
Few commentators expected the Black Cats to improve their situation to any meaningful degree as they headed for City, Chelsea and Manchester United either side of a home game against Cardiff.
But a surprise draw at the Etihad Stadium - but for a late error by keeper Vito Mannone, they might have won there too - heralded a run of three successive victories, two of them famously at Stamford Bridge and Old Trafford, which have lifted them to the brink of salvation.
Poyet said: "The problem is if you use the word 'surprised', it looks like you cannot believe it.
"I was getting close to wondering what we needed to do to win a football game because we were, in my understanding, performing better even at home, but there was always something happening that meant we couldn't go on and achieve the results.
"Maybe the first goal at Manchester City after two minutes gave the team something that was missing to go on and start performing and winning.
"We are on a run now and we don't want to stop
We want to keep playing and winning."
West Brom head coach Pepe Mel has vowed to fight his corner ahead of next week's talks with chairman Jeremy Peace.
Following his arrival in early January as successor to the sacked Steve Clarke, Mel has upheld his side of the bargain by keeping the Baggies in the Barclays Premier League.
Although Albion are three points above the relegation zone, their vastly superior goal difference over Norwich means they are safe barring the most astonishing sequence of results.
With two games remaining Spaniard Mel can face Peace, along with sporting and technical director Richard Garlick, pointing to the fact he has done all that was asked.
Whether Mel has done enough to convince them he deserves a new deal remains to be seen, especially given the rumours of unrest behind the scenes.
But then whatever Peace says when it comes to cash for the summer and the club's transfer policy may not be music to the ears of Mel, who signed an initial 18-month deal with a break clause inserted after the first six.
With talks planned for next Monday, Mel said: "When a manager comes in mid-season it means a club is having some difficulties.
"The most important thing from my tenure here was to get the team out of trouble.
"So my ambition, when I first came here, was that come the 12th of May West Brom would be in the Premier League, so I have achieved my maximum ambition.
"Now I have a different ambition
What I want to carry on is (for the club) to keep on improving
That's how I want to move forward in the future.
"Now I need to listen to what the chairman has to say
I want to know what he has in mind for the future of this club, what are his plans.
"But I also want you to understand I'm an ambitious person and I want to be able to put forward my own arguments to take this club forward."
Albion can at least afford to relax a little against a Sunderland side who have won their last three games to virtually secure their own place in the top flight for next season.
Despite that, Mel said: "What they've done is completely unexpected.
"No one thought Sunderland would be able to do that, but they have shown they've great mental strength
They fully deserve to stay up.
"For us, this is still a massively important game
We want to show our respect to the competition, the oppostion, so our only focus will be to win."
Mel has a doubt surrounding defender Steven Reid, who missed Sunday's 1-0 defeat at Arsenal with a groin injury.
Source : PA
Source: PA