Richards curled home a superb free-kick in the second minute of stoppage time to seal a famous 4-3 win for the Valiants.
Dean Glover's side were 3-1 down with 11 minutes remaining before goals from David Howland, Louis Dodds and Richards turned the match on its head.
This was Vale's fifth win in seven matches since Glover replaced Lee Sinnott in the managerial hot-seat in October.
Huddersfield should have gone ahead after 15 minutes but Phil Jevons steered his shot off-target when well placed.
Against the run of play, Port Vale broke the deadlock on 27 minutes.
Huddersfield's Joe Skarz back-pass was intercepted by Dodds, who rounded goalkeeper Matt Glennon and tapped home.
Huddersfield pressed for an equaliser, with Robbie Williams and Michael Collins both denied by the agility of Vale's shot-stopper Joe Anyon.
However, the hosts drew level a minute before half-time when Collins rifled home Gary Roberts' centre from seven yards out.
Moments after the restart, Ian Craney put Huddersfield ahead after racing past John McCombe and dispatching a shot beyond Anyon.
The game looked over when Williams ghosted in unchallenged to meet Roberts' corner and nod past Anyon with 25 minutes remaining.
But Port Vale refused to lie down and Howland made the most of an Andy Butler mistake to delicately chip Glennon on 79 minutes.
The visitors never gave up and scored an equaliser on 85 minutes as Dodds latched on to a Lee Collins' long ball to drill a left-foot piledriver into the bottom corner.
Huddersfield almost grabbed a winner three minutes later only for Butler to direct a header over the top when it looked easier to score.
It seemed that Port Vale had blown their chance to seal a sensational comeback when Howland blazed over the bar in stoppage time, before Richards' late intervention.