Timothy Fosu-Mensah's headed own goal was Town's first at home this season and lifted them off the bottom of the table at their opponents' expense.
It had been 659 minutes since Huddersfield found the net on home soil - through Tom Ince's injury-time winner against Watford on 14 April - and it was reward for a performance that showcased energy and endeavour in the first half and discipline and commitment in the second.
"This is huge for us," said Wagner, who was celebrating the third anniversary of his appointment as head coach. "We have the winning feeling back. For sure it is one of the most important wins we've had in the past three years. Everybody needed this belief back. It's massive for us.
"When you look at the fixtures in front of us, they are teams in and around the area where they'll be open games. Today I think we were the team who really wanted this win."
Fulham weren't in the game before the break and while they improved after that, they have now equalled a Premier League record by conceding 29 goals in their opening 11 games.
Monday's defeat was the Cottagers' fifth in a row and exacerbates what has already been their worst ever start to a top-flight season.
This is represented in their new league position, which sees them level on five points with Cardiff and 20th courtesy of the league's worst goal difference.
Huddersfield remain in the bottom three and are just a point and two places above Fulham, but will be buoyed by their superiority over a relegation rival and a first victory in 15 top-flight matches.
Town off the mark
Huddersfield set the tone for the evening in the early stages, dominating possession, pressing high and snapping into tackles to win the ball back whenever Fulham threatened to counter.
It quickly became clear that this was a fragile Fulham side, stripped of confidence and there for the taking, which the Terriers almost did when the tireless Jonathan Hogg dispossessed Aleksandar Mitrovic in midfield to set up Philip Billing for a 30-yard drive that struck the crossbar.
Undeterred, the Terriers stuck to their positive game plan and were rewarded when Fosu-Mensah beat Schindler to the ball but succeeded only in heading it in just before the half-hour mark.
Town were facing the prospect of becoming only the second side in English Football League history to fail to score in their first six home games of a season, joining Mansfield who failed to score in their first nine in the third tier in 1971-72.
It was a good time, then, to face the top division's weakest defence.
he home side were understandably less forward-thinking as the second half wore on, focusing all their efforts into a defensive display that helped them manage and see the game out without conceding.
"I don't care who scored it or how we performed," added Wagner. "People know we can perform better. The pressure was on for both teams but how we fought... we left everything on the grass.
"It was deserved. In the first half, we were clear, and in the second half we were able to keep them away from our goal."
Where do Fulham go from here?
Having spent £100m in the summer following promotion, they have acquired the necessary forward talent to help them stay up - not that they should much evidence of it here.
They did have the ball in the net in the second half, but Andre Schurrle's finish was ruled out as a result of Mitrovic straying unnecessarily offside.
And the German wasted a subsequent opportunity with a poor finish after he had broken clear down the left and had team-mates better placed to score.
However, such attacking errors pale in comparison to their inability to prevent goals going in at the other end, even against the division's bluntest attack.
It doesn't help that manager Slavisa Jokanovic still appears unsure of his best combination at the back, with Maxime le Marchand partnering Dennis Odoi in the manager's latest vain search for a clean sheet.
Their concession of 29 goals in their first 11 games means they emulate the unwanted defensive record set by Southampton in 2012-13. The Saints would go on to finish 14th that season but, on the evidence of this performance, such a recovery looks beyond the Cottagers.
"We're disappointed we didn't play well enough or show enough intensity, especially in the first 45 minutes," said Jokanovic. "We found some improvement but it wasn't enough to equalise.
"They must fight - this is a tough competition. There are 27 games ahead of us. We didn't show a positive reaction and we must be brave and look for improvement. At the moment it is not enough at this level."
Asked if he was concerned about his own position, Jokanovic said: "This is my job, that is it. I know in this kind of situation many things can happen but it is outside of my control.
"I will follow my plan and work with the team. I must find the solution. Other people, if they need to say something, they can use some words."
Man of the match - Jonathan Hogg (Huddersfield)
Terriers finally join the party - the stats you need to know
- Huddersfield ended a run of 14 Premier League games without a win (D5 L9).
- They are the final side in the top four tiers of English football to register a league victory this season.
- Fulham are the only Premier League side yet to keep a clean sheet in the competition this season, last registering a top-flight shut-out in April 2014 (1-0 at home to Norwich).
- Since the start of last season, only Manchester City, Tottenham and Leicester (five each) have benefited from more opposition own goals in the Premier League than Huddersfield (four).