Tom Pope headed the visitors ahead with a clinical finish in the fourth minute, the striker's 23rd goal of the season.
Midfielder Jennison Myrie-Williams added a second with a ninth-minute close-range strike before Liam Chilvers felled Sam Williams and he pulled a goal back from the spot.
Louis Dodds bagged his third goal in three games six minutes before the break, but Scott Doe's late strike left all to play for during a final frantic few minutes.
"It's a shame we couldn't get an equaliser, but we were always chasing the game after we conceded those early goals," admitted Daggers' boss John Still.
"But I was impressed with our second-half performance and the way the lads battled to get back into the game.
"We knew it was going to be tough because they (Port Vale) have had a great season, that's why they're top of the league.
"But we'd got back in the game with the penalty and then conceded at the wrong time before half-time. That was frustrating.
"The second-half performance was very good, though, and I thought we deserved another goal."
- Sports & Recreation
- Liam Chilvers
- Louis Dodds