Striker Paul Benson put the home side ahead from close range in the fifth minute, before Vale hit back just two minutes later when Marc Richards volleyed crisply past keeper Tony Roberts.
The visitors lost skipper Sam Stockley to a second yellow card in the 80th minute but managed to hold out for a point despite late Daggers pressure.
The home side oozed confidence after two league wins on the trot, with the first chance falling to defender Mark Arber who saw his powerful third minute header tipped over the bar by visiting keeper Joe Anyon.
Benson reacted fastest to a loose ball in the box to give his side an early lead by firing past Anyon from point-blank range.
Vale struck back almost immediately when Stockley swung in an inviting cross from the right which Richards volleyed low past Roberts to level the score.
The Daggers looked nervy at the back, with Vale forward Ross Davidson taking advantage of slack marking on the edge of the box to thunder inches wide in the 18th minute.
Dagenham striker Ben Strevens came close to retaking the lead for the home side in the 21st minute when he tried to spear the ball past Anyon from a Sam Saunders free-kick, only to see the keeper claw the ball to safety.
The home side came close to retaking the lead in the 32nd minute when Benson slammed the ball onto the crossbar from 10 yards after racing onto a Saunders through ball.
Benson left defender Lee Collins for dead in the 62nd minute when he raced into the box before firing straight at Anyon from a tight angle.
The striker hit the woodwork for a second time in the 68th minute when he nodded onto the crossbar from another Saunders cross.
The Daggers upped the pressure after Stockley was shown a second yellow card with ten minutes left, but were unable to find a way past the Vale defence.