The Red Imps came to London high on confidence after two league wins in a row, but were sunk by a dramatic late winner from Paul Benson.
The home side looked hungry from the start with frontman Chris Moore coming close to opening the scoring in the fourth minute, when his powerful 25-yard strike flew inches wide of the post.
The Lincoln defence was sliced open again in the 20th minute by midfielder Sam Saunders, who fluffed his shot after bursting onto a Ben Strevens through-ball.
Midfielder Dany N'Guessan came close for the visitors in the 35th minute when he skinned Daggers full-back Danny Foster for pace, but the Frenchman fired wide from 20 yards.
Lincoln piled on the pressure at the end of the first half with Dagenham keeper Tony Roberts pulling off a spectacular one-handed save to deny Mark Stallard in the 41st minute.
Stallard had a gilt-edged chance to put his side ahead two minutes after the break, but shot straight at Roberts after finding himself in acres of space at the edge of the Dagenham box.
Daggers upped the tempo with Strevens skimming Lincoln keeper Alan Marriott's crossbar with a dipping strike in the 52nd minute.
Marriott pulled off an acrobatic save to stop a thunderbolt header from Dagenham skipper Anwar Uddin in the 59th minute.
N'Guessan should have grabbed the lead for Lincoln in the 63rd minute when he outpaced the Dagenham back-line, but saw his low strike palmed wide by Roberts.
The home side brought on talisman Benson in search of a winner and the striker had an immediate impact when he thundered a 25-yard strike against the post in the 68th minute.
Benson looked hungry for goals and snatched an historic win for the Daggers in the 87th minute, when he rose highest in the Lincoln box to power home a bullet header.