The result leaves Daggers three points clear of the relegation zone
Midfielder Mitch Brundle looked to have rescued a point for the hosts with a close range finish 10 minutes from time but Alex Whitmore headed home in injury time after Daggers failed to deal with a free-kick.
In a first half of few chances, Daggers were the better side, dominating possession and spending much of the time in the Fylde half.
But it was the visitors who had the better chances, with Daggers goalkeeper Elliot Justham called into action on several occasions.
Barely a minute in, the stopper got down well to collect a low cross from the Fylde right.
And ten minutes from half-time he was called into action again, diving well to his right to gather a shot from the edge of the box.
Daggers seemed to move up a gear as the half ended, with Sam Deering stealing the ball from a Fylde defender. His shot was blocked and visiting keeper Josh Lillis tipped Myles Weston’s follow-up round the post.
Just before the interval, Daggers won a free kick near the by-line on the left-hand side. Deering rolled it short to Brundle whose driven effort went just over the bar.
As the second half began, there was a quick change in emphasis, with Fylde looking to get forward straight away.
And it paid off as they were ahead within three minutes. The away side broke down their right and Justham parried the cross into the path of Tom Walker. The forward had the simplest tap in to give the Lancashire side the lead.
It could have been 2-0 on the hour, but Angelo Balanta made a crucial block on the line from a corner to keep the deficit to just one.
Brundle then shot wide twice from inside the box but it was third time lucky as he got on the end of Liam Gordon’s cross to draw Daggers level.
But there was heartbreak in injury time when Whitmore got to the loose ball to nod home for the win.
The result leaves Daggers 18th in the National League, three points clear of the relegation zone.
Hear from Daggers boss Daryl McMahon tomorrow on Time 107.5FM
Attendance: 1064 (14 away)