Rhys Murphy, Jai Reason and Chris Whelpdale missed a plethora of goal scoring opportunities in a strong first half for City, but it was Chris Flood's low shot after 70 minutes that sent the three points back with the visitors.
Chelmsford were on top early on and Murphy nearly put the home side one nil up inside three minutes. He beat the offside trap and beat a Slough defender to the ball but put his shot over the bar from a narrow angle.
Reason was put through with a lob over the defence by Murphy after 11 minutes, but despite taking the ball round Jack Turner in the Slough goal couldn't put the ball in the net from a similarly narrow angle to Murphy's previous effort.
Chelmsford were absolute in their dominance in the first half but just couldn't quite convert their chances into goals. This was encapsulated by Murphy's strong back post header that was goal-bound, albeit for a well positioned Slough Town defender clearing it off the line.
Slough's first chance of the game came after 30 minutes, with Warren Harris trying a bending shot from range. It went over and wide but was a warning to the Clarets who'd come a bit off the boil.
There was yet more frustration for the City fans in the 34th minute, as Tom Wraight's whipped cross from the left went straight through the box. To use a popular cliché, any touch and it would have gone in.
Within 10 minutes of half time Chelmsford had started using crafty tactics. Wraight played a corner short to Joe Anderson who squared across the 18-yard-box to Chris Whelpdale whose shot from the centre was deflected over. It was both a well engineered opportunity and a sign of Chelmsford's willingness to try anything to break the deadlock in a game they should have been winning by a handful of goals.
The goal just wouldn't come for Chelmsford, epitomised yet again by a Murphy chance: from another short corner and ping pong in the box the ball fell to the striker who chested it down before volleying onto the crossbar from just a few yards out. The disbelief throughout the crowd was palpable. In hindsight, that was the sign it wasn't going to be Chelmsford's day.
Going in at half time the atmosphere was one of utter bewilderment. The Clarets had had enough chances to be at least five or six nil up, while Slough Town looked happy to weather the storm and see if they could hold out for a draw.
Slough must've taken huge confidence from the half time scoreline, because they came out in the second period a side with more impetus - getting into attacking areas and forcing Chelmsford into errors.
The Clarets took about 15 minutes to find their momentum again, with Murphy getting a good strong shot in on Turner and Wraight working hard to produce crosses down the right.
Chelmsford were saved from an embarrassing goal by the offside flag in the 67th minute. Chris Flood's finessed shot was parried into the danger area by McDonald and another Slough Town player tapped in - luckily for the Clarets the linesman had spotted the infringement.
Chelmsford had themselves to blame for conceding in the 70th minute though as Chris Flood slotted home from inside the box.
City were trying hard for the equaliser and nearly found one with 13 minutes left to play, as Jazzi Barnum-Bobb crossed to the back post for Anthony Church who headed wide.
The Clarets probably should have had a penalty in the 82nd minute when Church was pushed over from behind. Referee Jason Richardson waved it off just to add to already mounting frustration.
City were rallying for an equaliser with four minutes of normal time remaining and went close with a couple of corners. Slough were packed so tightly and defending so deeply it wasn't looking like Chelmsford would be able to break through.
Slough Town proved resilient through added time and frustrated the Claret collective by taking the ball to the corner flag with mere seconds remaining of the game.