Former striker Jepson was fondly remembered as a promotion winner with Town a decade ago but he did former team-mate and now Huddersfield boss Peter Jackson no favours.
The Gills battled hard but Huddersfield had enough chances to clinch a first win in seven games but 12-goal top scorer Pawel Abbott was woefully out of touch.
Abbott and Andy Booth, who learned his trade alongside Jepson in the mid 1990s, should have hit the target but their finishing was poor.
Jackson has denied that Huddersfield's glamour FA Cup third round tie at Chelsea on Saturday has had no effect on his players.
But since Town were drawn at Stamford Bridge they have not won a game. They have taken just five points from the last 21 and slipped out of the automatic promotion places.
For Jackson, Saturday's cup tie cannot come quickly enough while Jepson can look forward to better times in 2006.
Gillingham should have gone ahead in the 16th minute when they had the Town defence stretched. Danny Spiller rolled a pass for the unmarked Paul Shields but he sliced wide.
Gary Taylor-Fletcher went to place his shot when power would have brought more reward and then Jon Worthington and Taylor-Fletcher got in each other's way and keeper Jason Brown dived in to block.
Abbott was on the end of a good move but Brown saved with his legs.
On the stroke of half-time Martin McIntosh's long ball was collected out on the left by Abbott. He sent over a cross but Taylor-Fletcher's header went beyond the far post.
After the break Abbott fired straight at Brown and was then put clear by Danny Schofield but Brown pulled off a good save low down.
Booth missed the target with two headers and Adnan Ahmed went close with a powerful drive from just outside the box.
Shields had Gillingham's best chance when he stepped around McIntosh but screwed his shot wide.