Huddersfield Town hit three goals in 11 minutes to book an FA Cup fourth-round berth for the first time since 2014.
Town dominated their League One visitors throughout, but going into the final 17 minutes, only had Jack Payne's first-half opener to show for their efforts.
However Kasey Palmer's deflected shot opened the floodgates with substitute Harry Bunn curling home the third before Payne notched his second from close range.
Town boss David Wagner handed a debut to forward Izzy Brown, his new loan signing from Chelsea.
The fourth-round draw is on Monday evening (7.10pm).
First Half
2mins: A neat Town passing move ends with Joe Lolley shooting over.
12mins:Philip Billing drives too high from distance.
14mins: Good work by Dean Whitehead to thwart Rigino Cicilia.
21mins: Vale keeper Jak Alnwick does well to save Mark Hudson's header from a Kasey Palmer corner.
25mins: Lolley's 20-yard shot is tipped wide.
28mins: Jack Payne is played in by Lolley and shoots home off the left-hand post. 1-0.
36mins: Billing is just wide from long range.
41mins: A deep Ben Purkiss cross is headed clear by Hudson.
44mins: Lolley shoots high and wide.
45+1mins: Palmer us well placed but puts his effort over after Jon Gorenc Stankovic plays him in.
Second Half
47mins: Palmer's shot is blocked close to the line.
53mins:Martin Cranie slots home but the flag is up for offside.
63mins: Palmer is just too high from distance.
70mins: Izzy Brown sidefoots just wide from Harry Bunn's cross.
72mins: Sam Hart clears a Payne effort off the line.
73mins: Palmer's shot is deflected into the net. 2-0.
79mins: Town keeper Joel Coleman saves from Kjell Knops.
80mins: Bunn, teed up by Tommy Smith, notches with a curling shot. 3-0.
84mins: Payne finishes a Tareiq Holmes-Dennis cross from close range. 4-0.
Line-Ups
Town: Coleman, Cranie, Stankovic, Hudson, Holmes-Dennis, Whitehead, Billing (Mooy, 67), Lolley (Bunn, 58), Payne, Palmer, Brown (Smith, 71).
Subs not used: Wells, Schindler, Hefele, Ward.
Vale: Alnwick (Santos, 59), Purkiss, Smith, Streete (Hart, 39), Knops, Taylor, Grant, De Freitas, Kelly, Cicilia, Thomas (Forrester, 75).
Subs not used: Pereira, Amoros, Shalaj, Tavares.
Referee: Geoff Eltringham (Co Durham).
