A hat-trick from Lee Molyneux saw 10-man Stanley over the line, with Peter Murphy sent off for collecting a second yellow card.
Ian Evatt grabbed a late consolation for the Spireites but Stanley ran out convincing winners.
"That was extra special," said Beattie. "I love the players, they are class, and I love working with them and the atmosphere in the dressing room is different class after the game.
"We threw ourselves in front of tackles, the players put their bodies on the line and I am extremely proud of them.
"Lee Molyneux scored three great goals - he has come back here on loan and he seems to be enjoying his football.
"His hat-trick epitomises the spirit and performance of everyone - we all dug in.
"I think we will need more than 50 points to stay up this season as the league is so tight but this is a stepping stone."