The win lifted Huddersfield, who before Monday had scored only four away goals this season, into 18th place on six points, with Fulham now bottom on five points after 11 games.
Huddersfield fans must have expected another frustrating night as they saw an early shot from Danish midfielder Philip Billing come crashing back off the crossbar in the 15th minute.
Having not seen their side score a league goal at home since a 1-0 win over Watford in April, the home fans finally got to celebrate when Fosu-Mensah headed into his own net under pressure from Christopher Schindler.
Celebrating the third anniversary of his appointment, Huddersfield boss David Wagner sent out his side to defend in the second half, and they had little trouble frustrating the visitors.
Fulham lacked creativity and despite Andre Schuerrle having a goal ruled out for offside, they barely managed to trouble Huddersfield keeper Jonas Lossl as they slumped to their fifth defeat in a row.
For both sides, tonight feels like a must win game. Huddersfield sit bottom of the Premier League without a win ten games into the season. Fulham, meanwhile, are on a run of five straight defeats and are shipping goals at an alarming rate.
Victory could prove a major boost for one of these teams. Huddersfield, you expect, will be aiming to start quickly. This is an opportunity for them to secure an elusive first victory, and to move into a healthier league position.
The old "relegation six-pointer" cliche has been frequently used in the buildup to this game. Tonight, perhaps, it is justified...
Ten minutes to go
It's eerily foggy at the John Smith's Stadium tonight. That might be a useful excuse for Fulham if they ship another three goals against the division's lowest scorers.
The teams are out and we're moments away from kick off...
After an impeccable minutes silence to remember those who lost their lives in the Leicester helicopter crash, we're underway. The home fans sounds up for this one.
Huddersfield 0-0 Fulham
It's been a slow, somewhat disjointed start. Both sides, understandably, appear to be easing themselves into the game. They know they can't afford any mistakes here.
Huddersfield 0-0 Fulham
Huddersfield goalkeeper Lössl almost gets himself into trouble. He receives a back pass and only just evades the attention of the onrushing Vietto.
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