After losing for the first time this season last week against Chesterfield, Wilder was delighted with the reaction from his charges as Ryan Williams, Deane Smalley and Asa Hall grabbed goals for the high-flying U's.
"It was a tough day, against tough opposition. People were looking at our first defeat of the season last week - rightly so - and asking how we would react to it," he mused.
"Losing two key players in Dave Kitson and Andy Whing made things more difficult but the players showed a fantastic reaction, it was a big result, a big performance for us.
"Ryan Williams came in and scored on five minutes, a dream start for him. We then could have taken the game away from the opposition and took control. We knew they would come back at us fighting and showing a reaction as they are on a bit of a good run, they've had some good results of late.
"And we were the architects of our own downfall in that period. We conceded too many free-kicks and they punished us with one of them."
Williams swept in a low shot on five minutes, nearly finishing from 16 yards.
The U's dominated the opening half, but Pools levelled on 47 minutes when Luke James netted from close range.
A counter-attack on 67 minutes saw the visitors back in front as striker Smalley picked his spot.
And, in injury time, keeper Scott Flinders tripped Scott Davies in the area and Hall slotted in from the spot.
Wilder added: "Their goal gave them impetus and momentum. But we stemmed the tide and scored a good goal on the counter attack. Fair play to Asa Hall- he played a new role for us, did a job very well and won the points for us.
"We took our chances when they came which was pleasing. But to score at the end like we did, it's a great time as it kills the game off."