The hosts appeared to have the three points already in the bag after three goals in the first 29 minutes as they steamrolled the Spireites.
But two quick-fire goals from Laurence Maguire and Tom Denton gave Town a lifeline before half-time.
Overall, the home side were by far the better side and deserved the victory.
"I am delighted,” Woodman.
“I thought we played some really good stuff, but it wouldn’t be us if we didn’t make really hard work of it.
"The game should have been dead and buried at 3-0. We switched off a couple of times and let them back into it.
"The goals were just us switching off, and this is the difference sometimes.
"The performance was great but it is just a shame we have waited this long to put four goals past someone.”
Bromley, who have reached the FA Trophy final, are 11 points off the play-offs with just four games remaining.
Woodman added: "We are where we are at the moment, there is a bit of disappointment we are not in and amongst that top six or seven but I think we have got to be realistic as well because we are building blocks here.”