Mooy played the full 90 minutes but the Terriers were denied all three points by their former midfielder, Jacob Butterfield, who levelled with two minutes to go to finally break the spirited Huddersfield defence.
The Terriers had led since Collin Quaner's strike in the ninth minute but Butterfield, who played 50 times for the Yorkshiremen in the 2014-15 season, rifled an unstoppable effort past Danny Ward on 88 minutes.
Huddersfield, who registered just one shot on goal, had defended resolutely throughout to frustrate the Rams.
The draw leaves the Terriers in fourth place, seven points behind second-placed Newcastle with a game in hand and five points inside the play-off places. They also cannot catch leaders Brighton, who beat Wigan earlier in the day.
Quaner expertly slotted home Martin Cranie's cross on nine minutes for his second goal in as many games as Huddersfield got off to the perfect start.
Darren Bent was denied an instant equaliser when his header was chalked off for offside.
The Rams enjoyed an excellent spell of possession for the next 20 minutes but were unable to breakdown the solid Town defence.
Bradley Johnson scuffed a shot on the edge of the box after the ball fell kindly on 36 minutes.
Christopher Schindler hacked the ball away from inside his six-yard box as Ikechi Anya's whipped cross flashed across goal and Matej Vydra hit an effort wide in stoppage time when he should have done better after a quick free-kick caught the Terriers defence napping.
Derby won two quickfire corners early in the second half as they came out with renewed fight and Ward tipped Anya's shot around the post on 52 minutes as Huddersfield were pushed back.
Alex Pearce cleared from inside his six-yard box after Rajiv van La Parra's brilliant run and cross failed to pick out an attacker.
Derby again took charge of possession and territory, with Huddersfield happy to sit back and soak up pressure.
Bent smashed a free-kick well over for Derby on 75 minutes as chances remained few and far between.
Huddersfield were unable to make just their second corner of the game count on 80 minutes.
Bent headed Anya's free-kick over the bar with five minutes left while under pressure from two defenders but the equaliser finally arrived courtesy of Butterfield - though the celebrations would be loudest over 150 miles away on the south coast.
