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Having only replaced ex-Pools manager Neale Cooper on Tuesday, former assistant boss Jepson watched his side snatch a much-needed victory at Priestfield.
A ninth-minute goal from Paul Shields gave the home side the points in a game that never really captured the imagination.
Matthew Jarvis' precise pass set up Neil Harris and the former Millwall striker's shot deflected into the path of Shields at the far post, where he slotted his first goal for the club.
Gillingham looked hungry to reverse the poor run of form that had seen them drop into the relegation zone and had the chance to extend their lead when Harris just failed to convert a cross from the left.
Hartlepool struggled to find a foothold in the match and had to wait until the 40th minute for their first real chance, when Jon Daly looped his header just over the bar with Gills keeper Tony Bullock stranded.
The visitors came out strongly in the second period and Daly should have equalised after 56 minutes, but his header was brilliantly saved by Bullock following an inch-perfect cross by Richie Humphreys.
Martin Scott's side had several more chances to equalise as the half wore on, with the best falling to Thomas Butler following Daly's flick-on, but he screwed his shot embarrassingly wide.
It got worse for the former Sunderland player when he was sent off for his second bookable offence moments later.
Danny Spiller could have extended the home side's lead in injury-time but Gillingham will be thankful for this win which took them out of the bottom four in League One.