Saints struck first after the break through Danny Ings, leaving Steve Bruce’s men trailing with just over 35 minutes remaining.
But Andy Carroll’s introduction from the bench sparked a late fightback, as the frontman’s deep cross was nodded home by Jonjo Shelvey to restore parity.
And defender Federico Fernández thumped home the winner after Southampton goalkeeper Alex McCarthy spilled Sean Longstaff’s strike with three minutes remaining, giving United the victory that lifted them up to tenth in the Premier League table.
Midfielder Hayden, who was quietly effective in the middle of the park, says the Magpies deserve credit for their response after what was an underwhelming first hour against Ralph Hasenhüttl’s men.
“We didn’t get started in the first half – it certainly wasn’t my best game in a black and white shirt, I’ll give you that – but sometimes when it’s like that you just have to stick with it, keep running, keep working hard and hopefully something will fall for you,” the 24-year-old told nufc.co.uk. “Today we were by no means (at) the levels we’ve been at in the past few games, but sometimes you hear the big teams have gone to places and won ugly. We’ve done that today.
“It’s definitely a skill to have, because we were nowhere near it really first half, but second half we came out with a bit more spirit, a bit more fight and a bit more desire to get forward and create chances.
“Jonjo’s on fire at the minute, and it was a great ball from Andy, and then obviously Fede got another goal. We’re not too bothered where the goals are coming from, but we keep getting results, which is the most important thing.”
Hayden added: “I think we’ve got a mentality now where, even if we do go a goal behind, I think maybe if it was a couple of years ago we wouldn’t have won today or we wouldn’t have drawn – we might have panicked a little bit.
“But I thought we stayed calm in the second half, we knew there would be opportunities, and it was up to us to take them. Credit to Jonjo and Fede for the two goals.”
United are now in the top half of the table for the first time this term, and Hayden insists Newcastle have retained belief in their approach throughout the season so far.
“It’s just proving it, I think,” he said. “In the dressing room I think everyone’s had belief that we can do what we’re going to do. We get a lot of stick from a lot of people, saying certain things about style of play or possession or whatever it is, but at the end of the day, this is what we do.
“I think a few years ago, if you look at Burnley, people were saying the same thing about them when they finished seventh – ‘they just have no possession, the least passes’, stuff like that. It’s irrelevant – at the end of the day, it’s about winning football matches. That’s what we’re doing at the minute.”
Newcastle – who could even climb as high as fifth with a win at Burnley on Saturday – are now undefeated at home since their first outing of the campaign against Arsenal in August.
“And even on the opening day it was only a 1-0 loss and we were unlucky, really, to concede the way we did,” says Hayden. “But it’s just about taking each game as it comes now. It’s been a tough week, and I think we’ve not really made too many changes to the side from playing Manchester City, where everyone’s stats were ridiculous because you have to run a million miles, and then Sheffield United away – another tough, tough game with a lot or running. Today we were always not going to be 100 per cent because they had an extra day of recovery, but there was no excuses – we still got the job done.
“It’s just about recovery now, and getting ready for Burnley. It’s another chance for us to get three points, another team around us, and it’s a tough place to go again. We’ll get ready for the battle.”
