Australia midfielder Mooy played a full game but it was Norway international's Stefan Johansen's first-half double which helped Fulham to a fourth successive win and denied Huddersfield a victory which would have clinched a play-off spot.
Huddersfield had taken the lead through Chris Lowe's early penalty but goals from Scott Malone, Tom Cairney and Johansen left the home side reeling at 4-1 down at half-time.
Fulham inflicted Town's heaviest league defeat at Craven Cottage - a 5-0 drubbing in October - and made it nine goals in two matches against the West Yorkshire side.
It started well for Town when, in the fourth minute, Floyd Ayite pushed Lowe in the back and referee Andy Davies pointed to the spot.
Lowe picked up the ball himself and confidently struck the penalty left-footed into the bottom right corner.
Fulham hit back immediately and Johansen set up Ryan Sessegnon who fired over.
Ayite made amends for conceding the penalty when he set up Malone for the equaliser in the 16th minute.
Malone still had plenty to do and side-stepped a defender and fired across goal and into the far corner.
Four minutes later Fulham were ahead when Jonathan Hogg brought down Ayite and Cairney sent Danny Ward the wrong way from the penalty spot.
Fulham were well on top and Ayite forced a save from Ward before the Cottagers made it 3-1 in the 36th minute.
Sone Aluko broke from the halfway line and slipped a ball to Cairney. He set up a shooting chance for Sessegnon but his effort was blocked. The rebound fell for Johansen to drill home.
Johansen then made it 4-1 in the 45th minute when he caught Hogg in possession. He drove forward into the box and fired past Ward into the bottom corner.
Huddersfield almost grabbed a lifeline at the start of the second half when Mooy's persistence set up Rajiv van La Parra but his curler was just wide.
Fulham could have sealed it in the 54th minute with a quick fire breakaway move. Cairney played Sessegnon through the middle but Ward, one-on-one, made the save.
Town then brought on attacking subs Izzy Brown and Sean Scannell for Joe Lolley and Philip Billing as head coach David Wagner attempted to salvage something.
Fulham were happy to keep Huddersfield at bay and when Town striker Collin Quaner had an opportunity he was denied by Marcus Bettinelli.
Ten minutes from time Fulham had another great chance involving a slick passing move but Malone dragged his effort wide.
Johansen limped off injured with four minutes left but his job was done in the first half.
