So Huddersfield Town can win a cup-tie - and score more than twice in a match.
The former hadn’t happened since August 2014, the latter since March (remember that sweet 4-1 success at Leeds United?).
The League One visitors managed to hold Town to the one goal, scored by the lively Jack Payne just before the half-hour mark, until the 73rd minute.
But after Kasey Palmer’s shot was deflected in, Vale lost their way.
Substitute Harry Bunn struck with the best goal of the game before Payne completed a fine display with his second of the afternoon and third in Town colours.
That’s eight matches unbeaten for Town and six wins in that enjoyable spell - successive clean sheets have also been recorded for only the second time this season and the third under Wagner’s stewardship.
With a decent 11,715 crowd inside the John Smith’s Stadium - and credit the 1,508 Vale supporters who helped create a good atmosphere - it was a pleasing afternoon all round.
And one of the most encouraging aspects was that victory was sealed without Wagner’s biggest hitters - a good sign of the state of the German’s squad.
The seven players who had made the most starts were all missing from the third-round XI: Elias Kachunga (26) and Chris Lowe (22) were rested altogether while Danny Ward (25), Aaron Mooy (25), Christopher Schindler (24) and Tommy Smith (22) were on the bench.
And Jonathan Hogg (21) was again ruled out with a thigh injury.
Wagner hopes both midfielder Hogg, who has missed three games, and wideman Rajiv van La Parra, out for two with a knee problem, will be back in training on Tuesday.
And of course he also has a new forward in Chelsea loanee Izzy Brown, who was handed a starting spot and showed enough to suggest he will prove a good acquisition.
While there were five changes after the 1-0 Championship win at Wigan Athletic, Town stuck to pretty much their usual formation and full-throttle approach.
Brown went wide left with Joe Lolley on the right, either side of Wagner’s two ‘number 10s’ Palmer and Payne, who completed a fluid set of forwards.
It was noticeable how Vale were denied space and possession by the home side’s keen pressing as well as accurate passing.
The pressing took place all over the pitch and combined with the passing, helped create a succession of chances.
Town would have been better off at the break had it not been for visiting keeper Jak Alnwick, who made fine saves from Mark Hudson and Lolley, who made a first start since August after his foot injury.
And before Palmer doubled the advantage, Brown came agonisingly close to celebrating his 20th birthday with a goal while Payne had an effort cleared off the line.
Town had string-puller Mooy on the pitch while Alnwick, who collided with a post when making that stop from Hudson, had been replaced by Portuguese keeper Miguel Santos by the time the goal flurry came.
But there was no compelling case for either change making a huge difference, because Town were well on top.
Now fans can enjoy the build-up to the fourth-round draw (Town will be ball number 25) and dream of a big tie.