The Shots fell behind to an early Halifax strike through Killeen, but drew level when Holloway burst through the Halifax defence to score.
Aldershot went ahead through Griffiths' first of the afternoon in first-half injury-time, before rounding off the scoring in the 73rd minute.
The hosts were playing their first game in three weeks, after a break which manager Terry Brown described as a "blessing in disguise". Several of Brown's key players were able to shake off knocks, enabling the Shots to field a full-strength side.
Halifax made a lively start and were almost ahead in the second minute, when Killeen fired just over the bar.
The Shaymen were able to keep possession with some intricate play, which the Shots seemed happy just to watch.
Aldershot had a good shout for a penalty in the seventh minute. Ryan Williams crossed for Tim Sills, but his header was parried by Adam Legzdins and Griffiths' follow up shot seemed to hit a defender's arm, but no spot-kick was given.
Halifax took the lead on 16 minutes with a well-worked move from the left. Chris Senior and Danny Forrest combined to set up Killeen, whose precision strike from the left found the target, leaving Nikki Bull rooted to the spot.
The lead lasted all of six minutes, as the gutsy Shots drew level through Holloway. Nick Crittenden crossed for Sills, and with the Halifax defence unable to clear, Holloway thundered through the middle to place the ball wide of Legzdins.
Griffiths was in menacing mood, and when he latched on to John Brough's throughball and got behind Greg Young in first half time added on, he put the home side ahead.
The Shots went further ahead through Griffiths' second. Crittenden's corner was swung on to Brough's head, but was saved on the line by Legzdins, only for Griffiths to pounce on the rebound.
Despite late efforts from Senior, Forrest and substitute Justin Bowler for Halifax, Aldershot held on for the three points.