Fosu-Mensah headed into his own net, under pressure from Town's Christopher Schindler as Huddersfield halted an eight-game home run without a top-flight goal – and moved above Fulham and Cardiff at the foot of the table.
The Terriers' winless league run stretched back to April – 14 league games in total – but manager David Wagner was able to celebrate on the night of his third anniversary in charge with a morale-boosting victory.
Fulham's fifth successive league defeat did little to ease the pressure on boss Slavisa Jokanovic, whose side's own run without a league win was extended to eight matches.
Huddersfield almost halted their barren spell in spectacular fashion when Philip Billing's 30-yard thunderbolt struck the crossbar in the 15th minute.
Steve Mounie headed Aaron Mooy's cross tamely over soon after and Alex Pritchard's brilliant effort from outside the area was expertly clawed away by Fulham goalkeeper Sergio Rico.
But Huddersfield's agonising wait for a goal at the John Smith's Stadium was finally over in the 29th minute, making it 659 minutes in total.
Chris Lowe crossed deep from the left and German centre-half Schindler saw his header deflect into the net off Fosu-Mensah.
Jonathan Hogg almost pierced the Premier League's leakiest defence again just before the break, but his looping header was saved by Rico.
It was the 29th goal conceded this season by Fulham, who did not manage a single effort on target before the break, such was Huddersfield's whirlwind first-half performance.
Fulham boss Jokanovic sent on Kevin McDonald and Cyrus Christie for Luciano Vietto and Fosu-Mensah at the interval and the Londoners began the second half with more intent.
Christie's cut-back was cleared behind by Hogg and Mooy headed away the corner.
The Terriers continued to harry and chase and Pritchard fired narrowly off target in the 68th minute.
Substitute McDonald had been forced out of the action due to a knock – but Fulham began to make a fist of it.
Schindler blocked Aleksandar Mitrovic's shot and Andre Schurrle's effort was ruled out for an offside decision against the former in the 74th minute.
Schurrle shot off target again, while Town substitute Isaac Mbenza also spurned two half chances when sent through on goal in the closing stages.
Town were not to be denied however – and the first top-flight meeting between the two sides since 1952 ended in their favour.