John Still's side have now taken 10 points from their last four games after Lewington dived to his left to beat out Richards' spot-kick after Charlie Wassmer had fouled Tom Pope.
Richards and Louis Dodds had shots saved by Lewington as Vale made the early running. But the remainder of the first half didn't live up to a promising start and it was the visitors who threatened next a minute before the interval.
Medy Elito curled a 20-yard shot past Vale keeper Stuart Tomlinson, who was relieved to see the ball strike the inside of his right-hand post and roll to safety.
Vale struggled to break down Dagenham's defence at the start of the second half and manager Micky Adams introduced Tom Pope and Paul Marshall just after the hour.
But it was Dagenham who made the decisive breakthrough in the 65th minute when Micky Spillane buried a six-yard header into the roof of the net from Damien McCrory's right-wing free-kick.