Mooy picked up his seventh assist of the season when he drilled in a perfect corner kick that defender Michael Hefele was able to head straight past Barnsley's keeper.
Huddersfield dominated the match but were unable to convert their numerous chances due to some great last ditch defending by Barnsley.
Mooy was once again the most involved player in the game, having more touches (88) and completing more passes (60) than anyone on the pitch.
The former Melbourne City midfielder's performance wasn't all positive though, he managed to pick up a yellow card in the first half for a heavy challenge on Josh Scowen.
Huddersfield, who have only lost one of their past 17 matches, remain in third spot on the Championship table, four points and a game in hand clear of Leeds United while five points short of second placed Newcastle United.
Fellow Aussies Callum Elder and Ryan Williams both started on the bench for Barnsley, with Williams coming off the bench in the 93rd minute as the Tykes held on for a point.
Elsewhere, Massimo Luongo was an unused substitute in Queens Park Rangers' 2-1 loss to Preston North End. As was Brad Smith in Bournemouth's 2-1 loss to West Brom.
Mile Jedinak played the full 90 minutes in Aston Villa's 1-0 win over Derby, creating one chance and making four interceptions.
Bailey Wright also played a full match as his Bristol City recorded a surprise 2-2 draw with high-flying Newcastle at St. james' Park. Bristol are currently just one place above relegation.
In the Dutch top tier Jason Davidson had a roller-coaster match, setting up Groningen's second goal to give them a 2-0 lead only to see it evaporate in the second-half and lose 3-2 as well as pick up a yellow card in the process.