Despite going a goal behind, the Bees completely outplayed their Kent rivals and will now eagerly anticipate Sunday's second round draw.
The first half started at an intensity worthy of the FA Cup, although neither side could produce a serious threat on goal. Barnet were clearly comfortable and dominated the opening half-an-hour.
In the tenth minute, Adam Birchall stole into the Gillingham box and fired at goal from ten yards, but Simon Royce did well to parry the drive to safety.
Two minutes later Jason Puncheon delivered a dangerous ball into the box, a goalmouth scramble ensued and Efe Sodje was forced to desperately clear the danger.
Mark Stimson's side were forced into a rearguard action again on 23 minutes. Ashley Carew went on a driving 60-yard run and crossed to Puncheon, and but for a timely intervention from Nicky Southall, the Barnet winger would have had the easiest of chances.
Even though Barnet had controlled most of the first half, the Gills took the lead on 27 minutes. Slack marking from Puncheon deep in his own half allowed Southall to cross to David Graham, the former Sheffield Wednesday striker, who rose highest to bury his header past Lee Harrison.
Gillingham were still off the pace in the second half. Sodje cleared off the line from Birchall's 46th minute cross, before Barnet's determination finally told on the hour mark.
Royce failed to deal with Josh Wright's free-kick on the right and Ismail Yakubu headed home from inside the penalty box. Barnet doubled their lead two minutes later when Liam Hatch crashed his seven-yard header home from Kenny Gillet's cross.
Gillingham's response was immediate. In the 65th minute Delroy Facey's 20-yard drive was deflected off the line by Joe Devera. Despite competing against a side a division below them the Gills' performance was surprisingly listless.
Barnet closed out the game in the ascendancy. Puncheon's 25-yard drive flew narrowly over the bar after he'd beaten three players, and even the late dismissal of Carew could not negate a thoroughly deserved and dominant victory.