The Glovers came out second best in a five goal thriller at the Chigwell Construction Stadium.
On a blisteringly hot afternoon, the hosts almost took an early lead when Angelo Balanta struck the woodwork against his former employers before chances then dried up.
With 10 minutes of the half remaining, Rhys Murphy forced a good save to mark the visitors' best chance of the half before Town's number nine opened the scoring just 20 seconds into the second period.
Perfectly placed to head home Charlie Lee's pinpoint cross, the opening goal was cancelled out by Joe Quigley's response on 64 minutes.
Triggering an assault on either goal, Manny Onariase turned the game on its head as the game entered the final 10 minutes but for Matt Worthington to issue an instant response just 60 seconds later to drag the Glovers back into things.
In a breathless second half the drama wasn't complete as in the 94th minute Quigley doubled his tally for the day to secure an unlikely three points for the hosts.
Looking to end a run of back-to-back defeats, Darren Sarll made three changes for the trip to the capital which included a forced change between the sticks.
Stalwart Stuart Nelson picked up an injury to see him miss the trip altogether, handing QPR loanee Marcin Brzozowski a first start for the club.
Featuring from the bench on Saturday after returning from injuries, defender Luke Wilkinson was given a first start for the green and whites whilst former Dagger Murphy came into the side.
After losing out in a slow tempo affair at the weekend the meeting at the Chigwell Construction Stadium started in blistering fashion as former Glover Balanta clipped the top of the crossbar with a scooped effort from an acute angle after just three minutes.
With Peter Taylor's side looking to stamp their authority on proceedings inside the opening 10 minutes, the visitors survived the early scare to grow into the game.
Holding the Daggers' at arm's length it became a tense tactical battle as the two 3-4-1-2 formations cancelled each other out.
Making his first National League appearance, Brozozowski continued to have a gentle introduction to the division as his counterpart Justham wasn't tested until the 34th minute.
As the temperature snuck above 30 degrees celsius, Murphy looked to raise excitement levels in the away end as his quick-fire curling shot from the edge of the box had to be pushed behind for a corner which resulted in Wilkinson then having a goalbound shot blocked from six yards.
With that flurry marking the Glovers' best attacking output of the half it remained goalless at the break as the visitors ended brightly.
Having built up a slight head of steam before the referee's whistle drew a halt to proceedings, Sarll's side wasting no time in taking the lead following the restart.
Lee's midfield run was spotted perfectly and his resulting cross was perfect for Murphy to head home his second of the campaign.
Looking electric upfront, the former Dagger almost grabbed a second soon after when his shot on the stretch following a bursting run into the box was kept out by a firm Justham hand.
Sparking an immediate response from the home bench in the form of a double substitution, one of those introduced almost levelled it up.
James Dobson's first touch was a rasping strike from the edge of the box that Brzozowski did well to palm away from danger.
With the game now opened up into an end-to-end affair Murphy continued his personal assault on the Dagenham goal as his acrobatic volley from a Remeao Hutton cross flew just over the bar on the hour-mark.
However, reinvigorated following the changes the hosts drew level when Alex McQueen's whipped in delivery was all the invitation Quigley needed to restore parity to trigger a hectic spell.
Just two minutes after drawing level the Daggers hit the woodwork once more when Balanta was once again denied by the crossbar, instantly followed by Murphy forcing Justham to tip his dipping strike over the bar.
Now into the final 20 minutes the shots on goal continued to rain down as Worthington's venomous strike from the edge of the box had to be parried at full-stretch by the home stopper.
With the pendulum of momentum swinging from one end to the other, the Daggers turned the game around as the game entered the final 10 minutes when Onariase's header nestled in the back of the net.
But with the home supporters still celebrating taking the lead for the first time, they were pegged back when Worthington made no mistake from inside the box by blasting a thunderous effort into the roof of the net.
Introducing Myles Hippolyte in an attempt to retake the lead his cross was turned goalwards by Murphy which produced a world-class save from Justham in what looked to be the final twist of a whirlwind second half.
However, the Daggers stole all three points at the death when deep into stoppage time Quigley grabbed his second of the afternoon to leave the green and whites down and out in London.
Dagenham & Redbridge: Justham; Onoriase, Clark, Croll; Eleftheriou (Dobson 54'), Brundle, Robinson, McQueen, Graham (Luque 54'); Balanta, Quigley.
Subs not used: Gordon, Grant, Phipps.
Yeovil Town: Brzozowski; Skendi, Wilkinson, Bradbury; Alcock (Hutton 46'), Worthington, Lee (Whelan 67'), Dickinson; D'Ath (Hippolyte 79'); Duffus, Murphy.
Bookings: Wilkinson 14', Hutton 77'.
Subs not used: Rogers, Shako.