The young Magpies conceded twice in the opening 45 minutes, with Gabriel Kyeremateng and Daniel Jarvis finding the net for the Potters at the bet365 Stadium. However, Owen Bailey, who missed a first-half penalty for United, sparked the comeback with a header before substitute Yannick Touré levelled with a finessed strike.
Late drama unfolded as Bailey netted the match-winner, heading home from Matthew Longstaff's cross to grab his brace and cap off a memorable evening for the under-23s captain.
The result sends United into third place, who are now two points behind league leaders Southampton but Dawson reflected on both the positives and negatives from his side in the Division Two clash.
He told nufc.co.uk: "I think from the player's view they went from playing sloppy and lethargic to all of a sudden playing with some urgency and intensity in the second half, showing a lot of fight.
"It was really disappointing at half-time and we let the players know that but it was a fantastic response. It was a great experience for them to do that and I wish they could have done that for the whole 90 minutes as we could have made it so much easier for ourselves.
"We had a mountain to climb but this group has that character and the quality which we showed in the second half to be able to go and score three goals away from home in a 45-minute period. If other teams start looking at that and thinking the game isn't dead at two or three nil, that's always a good thing to have.
"There's a little bit of pressure off us now in the league but like every game we play in, we are playing to win it. We weren't playing to sit back and take a draw against Stoke knowing we would qualify for the play-offs. At 2-2, we were pushing another goal and after scoring, we were still going for a fourth."
United face Manchester United and Middlesbrough in their final fixtures of the season, aiming to continue their impressive season after reaching the Checkatrade Trophy last 16 and reaching the semi-finals of the Premier League Cup for the first time.
Although eyes will be fixed on securing automatic promotion to the top tier of Premier League 2, Dawson highlighted his squad have more than exceeded expectations from previous campaigns.
Dawson added: "To get promotion would be the icing on the cake but what we have achieved already this season outranks what we have done before.
"We've been close in the play-offs before but the added bits around this group such as seeing Sean's (Longstaff) acceleration (in Newcastle United's first team) is the biggest thing that the lads can see and grasp onto.
"Earlier in the season, he was one of them, playing games, and then all of a sudden he is making his Premier League debut away at Liverpool. The lads can see that if you have the effort, desire and qualities along with good habits and consistency in performance, you have a real chance."
