The visitors took the lead in exhilarating fashion as Chris Humphrey's superb cross from the right was glanced into the net by Grant Holt after 19 minutes.
Matt Ritchie came close to levelling the scores, but his goalbound effort was blocked and then Sam Saunders fired over from a good position.
Daggers keeper Tony Roberts saved well from Humphrey, but he had no answer after 33 minutes when the winger easily got clear and calmly lobbed him from close range.
After the interval, Daggers were denied a way back into the game when Paul Benson smacked a shot against the post, before Ben Strevens' rebound was superbly saved by Luke Daniels.
The hosts did pull one back after 53 minutes as a long Ritchie cross was headed home by Benson. Daggers huffed and puffed in search of an equaliser, but the closest they came was Saunders' low shot that bobbled wide.
League Two play-off semi-final fixtures: First legs: Shrewsbury v Bury, Rochdale v Gillingham (both Friday 7 May).
Second legs: Bury v Shrewsbury (Sunday 10 May, 12pm), Gillingham v Rochdale (Sunday, 10 May 6.30pm).