Superb goals in each half from Liam Mandeville and Jim Kellermann against the League Two hosts secured the Spireites’ place in the third round for the first time since 2015.
The victory is even more remarkable considering Town had 11 players unavailable.
“That was for everybody, the fans, the board who have trusted me in the last year,” Rowe said.
"We have got 11 players out and we are still performing like that and we got a clean sheet.
"I thought it was a fitting end to Jim Kellermann’s performance to score the second.
"Sometimes it is just how much you want it and I think we wanted it more.”
Mandeville opened the scoring on 28 minutes with a stunning strike which clipped the crossbar on the way in.
Kellermann doubled the lead with four minutes to go when he fired into the roof of the net.
"This is why we work so hard and put the hours in when no one is watching and this is what you sacrifice it for,” Rowe explained.
"The way we have come together in these last three weeks to pick up points and maintain first position and to come to a team that is in-form in League Two, to come away from home and keep a clean sheet is credit to the lads.
"We have got something special here and we want to keep hold of that and move forward but we have got to keep our feet on the floor, we have not won anything.
"We can’t take our foot off the gas now, we need to push down and push even harder to get to where we want to get to at the end of the season.”
One downside was an injury to Luke Croll in the first-half, who came off with a thigh strain, but it is not serious, Rowe said.
On Monday’s third round draw, Rowe added: "I am just going to enjoy my red wine, make sure it is a nice red, I think I deserve that, and sit with my son and my partner and watch it.”