The 20-year-old headed home a corner on his fifth appearance for the Valiants after joining the club on loan until the end of the season in January.
He spent the first half of this season playing under former Whites boss Simon Grayson on loan at Fleetwood Town. In 17 appearances, Edmondson found the net twice - both times in the EFL Trophy - before the Harrogate-born striker was recalled early in order to seek more game time elsewhere.
After a tough loan spell at the Highbury Stadium, Edmondson expressed delight at opening his Port Vale account.
“I think the video speaks for itself. I think as a striker, you claim everything you can, but to get off the mark for Vale is a massive thing for a striker," Edmondson said.
“I’m three or four appearances in now so to get off the mark this early is a great achievement.
"It’s a shame about the result, but on a personal note I’m very happy.”
The forward later reposted the video of his goal that Port Vale shared with the promise, "first of many".
Meanwhile, Cody Drameh's choice to pass up what Marcelo Bielsa deems a "great chance" within the Argentine's slim United squad is bearing fruit so far.
Former Whites striker Steve Morison has selected Leeds loanee Cody Drameh in his starting eleven for every game since the young full-back departed Elland Road in January to join Cardiff City until the end of the season.
Over on the south coast, Leif Davis is pushing to stake a claim in Scott Parker's starting eleven as Bournemouth continue their promotion charge.
The left-back started in defeats to Luton Town and Hull City before dropping to the bench for the Cherries' win over Barnsley at the weekend.
Elsewhere in the EFL, Alfie McCalmont made a strong start to the year when his assist gave loan club Morecambe the lead in the Shrimps' FA Cup tie against Tottenham Hotspur.
From a corner, the young midfielder floated a tempting ball into the six-yard box for Anthony O'Connor to tuck home with ease to give the visitors the lead at the Tottenham Hotspur Stadium.
Unfortunately, the Lancashire side couldn't hold onto their lead and Spurs advanced to the Fourth Round with a 3-1 win.
Across Europe in the past week, Kun Temenuzhkov made a six-minute substitute appearance at the close of Real Unión's league win over Celta Vigo B, while Hélder Costa remained on the bench for the second game in a row as Valencia were defeated by Atlético Madrid.
As captain of Zulte Waregem, Laurens de Bock is fighting to keep his team in the Jupiler Pro League as the Belgian side teeter on the brink of relegation, two points clear of 17th-placed RFC Seraing.
Whites goalkeepers have found mixed success abroad, with 20-year-old Elia Caprile keeping six clean sheets and starting all games but one for Aurora Pro Patria this season while Kiko Casilla hasn't featured in La Liga since October, though the shot-stopper kept two clean sheets in the Copa del Rey in December.
Mateusz Bogusz suffered huge disappointment last month after his flying progress on loan at UD Ibiza was cut short by a rupture to his anterior cruciate ligament. The Pole made five goal contributions in his three most recent La Liga 2 appearances before suffering the injury, which will require surgery and keep him sidelined for the rest of the season.