It was a result that continued the Dragons’ impressive surge and pushed them to within a single point of the Championship play-off places.
In a congested top half of the table, they are only six points behind the automatic promotion places.
Wrexham made it four wins on the spin with a display that underlined their growing belief.
“To get to 250 at any club, I’m very proud of that because management is hard but I’m really enjoying my time here,” Parkinson said.
“We’ve got great owners and I enjoy every single day. When you reach those milestones, it’s always great if you can celebrate with a victory.”
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Wrexham burst out of the blocks at Pride Park and could easily have been two goals clear before Sam Smith made one chance count in the 25th minute, finishing from close range after sustained early pressure.
Derby responded well and were back on level terms eight minutes later when Ben Brereton Diaz found space on the edge of the area and fired past the Wrexham goalkeeper.
But the visitors regained control early in the second half, Matty James producing a moment of real quality with a stunning strike from outside the box just three minutes after the restart.
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Parkinson was full of praise for James, who has featured in every league game for Wrexham this season and capped another tireless display with his first goal of the campaign.
“His performance was brilliant,” Parkinson said.
“You look at Matty, he's played every game over this Christmas period and he was so good today, so good.
“I'm very pleased for him to get that goal. It was a brilliant finish.”
Smith’s contribution was also singled out, with the striker continuing a run of influential performances that have been central to Wrexham’s recent success.
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“I thought at Blackburn he was really good. He did everything you'd want from a striker. He ran in behind, he held it up and he got his goal,” Parkinson said.
“Today, again, against good players, you're up against three really good Championship defenders, he's had a brilliant chance earlier, but then he got his goal.
“It's just his all-round play and the way he fought for the team was just brilliant.”
Beyond the individual performances, Parkinson stressed how much the collective spirit at the club meant to him as he reflected on reaching a significant milestone in his managerial career.
“There’s been a lot of expectation but it’s been an enjoyable journey so far because I’m working with great people, not just the staff but the owners and we are building another dressing room this year,” he said.
“We’ve always prided ourselves on getting that dressing room right and we are building another one of real strength and unity.”
He also felt the performance itself fully merited the result, particularly after the intensity with which Wrexham approached the contest.
“It’s a great win for us today. I’m so pleased with how we played. I thought we started the game really well and we had three incredible chances to take the lead and then we got the goal,” Parkinson added.
“We said we had 45 minutes to finish this little block of games and we needed to go and give it everything to finish on a high, and we were able to do that with a brilliant strike from Matty James.”
While Parkinson was keen not to overstate the importance of the club’s current run, he acknowledged that four straight wins over the festive period had left Wrexham in a far healthier position in the promotion race.
“We've certainly put ourselves in a stronger position after the Christmas period,” he said.
“It's four out of four over Christmas and I'm so pleased for our supporters because that support we had today was amazing.
“When you look at the costs over the Christmas period, for the supporters to come out in their numbers today was brilliant and I'm so pleased we sent them back happy.”
For Derby head coach John Eustace, the afternoon proved frustrating after a morale-boosting New Year’s Day win over Middlesbrough, with the manner of defeat particularly disappointing.
“I thought in the second half we would go on and at least not lose the game, but the way we lost was disappointing in the decision-making a couple of times,” Eustace said.
Despite the setback, he insisted his players’ attitude remained strong and pointed to the progress made under his leadership.
“This group of players will never give up, they’ll keep going to the end, which is all I ask from any group of players, that they show that level of commitment and desire and we certainly got that,” he said.
“I think we’ve made fantastic progress from when we came in, to be on this number of points now at this stage is really pleasing and this group of players have been fantastic, they’re learning and developing all the time.
“We are playing against teams who have good squads and we are going toe to toe with them and sometimes that lack of quality might cost us, but that desire and heart will get us a long way.”
