The Clarets trailed 2-0 at home to Borough but struck five in a rampant second half.
Church's two goals within two minutes set them on their way as Michael Spillane, Kudos Oyenuga and Chris Dickson went on to complete a sensational performance.
Chelmsford are fifth in the Vanarama National League South, two points behind leaders Braintree Town.
"Some words were said at half-time. The first-half wasn't good enough," said Church.
"That could be the turning point in our season, a lot of character was shown in the second half and we needed to.
"We're a new group of players, we're still finding our feet but to comeback showed a lot about us.
"We felt that at half-time we had nothing to lose. It's nice to get two goals but it's not about me. I'm glad I've done it for the team."
For more coverage, reaction and some of the best moments from games going throughout the season, head to our social media channels on Twitter, Facebook and now Instagram.