Goals from Andy Cook - who bagged his 18th of the season - a Daniel Lafferty own goal, and a Josh Gordon strike secured all three points for the Saddlers, allowing them to close the gap on many of their relegation rivals, taking their battle to beat the drop into this weekend's clash with Shrewsbury Town.
A win over the already safe Shrews, along with a couple of favourable results elsewhere, and the Saddlers should secure a spot in League One for at least another season, something which - thanks to a run of seven defeats in eight games - seemed highly unlikely just a few days ago.
And Bishopbriggs-born Devlin, who could make his 49th appearance of the season at the weekend, firmly believes the Saddlers have given themselves a great chance of securing survival, insisting they could well have scored more against the shell-shocked Posh.
Nicky, who was speaking via the club's official website, said; "We have given ourselves a chance and before the Peterborough game that is all we could do. We also had to hope things elsewhere went for us but they did. We created a lot of chances and I don’t think they could have complained if it went four or five.
"I had one, where I got ahead of myself a wee bit. I’ve scored the exact same goal three times this year so I have no idea why I didn’t just try and do it again. But it was good we were creating chances and that is a positive going into Shrewsbury.
"If we can create half as many chances there, we will have a shot. We have given ourselves a chance and going off the back of a 3-0, we should take confidence from that going into the Shrewsbury game. Peterborough’s squad, when you look on paper, is as good as anyone’s – especially going forward.
"To keep a clean sheet at this stage of the season, when there was so much pressure on the game, it was good. We’ve not done that since Fleetwood, which has been a long time for us. It’s good for the defence to build on that confidence-wise. And the attackers can build on getting the goals as well."
Although delighted with the welcome win, the 25-year-old admitted that he is a little frustrated he and his teammates hadn't been able to produce it in more games, as they'd probably be well clear of danger heading into the final game of the season.
Nicky continued; "If you perform like that – even in half your games – then the only pressure you’d have is how high you finish in the top half of the table. Individually, a lot of the players are frustrated that they haven’t produced that type of performance throughout the season.
"As a team, we haven’t been produced anywhere near enough like that. But against Peterborough, we did put in a great performance; it’s a struggle to think of a better one this season. Maybe it’s come just at the right time."