Ebbsfleet needed penalties to progress in the FA Trophy on Tuesday night.
The win sets up a trip to ex-Fleet boss Daryl McMahon's Dagenham side in the third round on Tuesday.
Rakish Bingham had come off the bench to head Fleet in front in the 73rd minute but Tom Harrison's brilliant injury-time strike took the game to penalties.
James Dobson, Jack Paxman, Bobby-Joe Taylor and Bingham all scored, with Joe Hanks hitting the bar and Luke Russe seeing his spot-kick saved by Tom Hadler.
This was the third time the teams had met this season. Fleet were knocked out of the FA Cup on penalties by Chippenham but got their revenge by bagging three points when the sides met in a National League South clash
Fleet made five changes from the team soundly beaten by Havant in the league on Saturday.
In came Michael West, Greg Cundle, Ben Chapman, Charlie Rowan and keeper Hadler, with West deployed as the main striker.
Indeed, West nearly set up Fleet's opener in the 14th minute but his cross-shot found Taylor at the far post. A combination of the post and excellent defending by Callum Gunner denied him.
Chippenham keeper Will Puddy then fumbled Toby Adebayo-Rowling's right-wing cross before another neat Fleet move ended with Cundle exchanging passes with Chapman before toe-poking wide from 10 yards out after declining a left-foot effort.
Chippenham had two excellent chances when Fleet gave the ball away. First Ross Stearn put his shot wide and then, after Paxman gave the ball away and failed to track his man, Brad Ash missed a similar chance on the stroke of half-time.
Fleet could have easily been ahead by then as Lee Martin twice called Puddy into action while the hosts felt Ryan Law was fortunate to escape with a yellow card for a foul on Cundle.
The game lacked the same quality in the second half, although Fleet improved defensively with Chippenham on the back foot for long spells.
The visitors were wasting time with more than 20 minutes left, presumably content to take their chances in a penalty shoot-out.
The breakthrough came with 17 minutes left. Substitute Dobson delivered a perfect right-wing corner and fellow substitute Bingham headed in from close range.
Fleet suddenly looked a team full of confidence as they started to spray the ball around, boosted by their first goal on home turf in four matches.
Ash fired wide with four minutes left for the visitors and Fleet looked destined to hold on until a stunning strike by Harrison.
The big centre-back turned and struck brilliantly inside the area after a long throw-in landed at his feet.
Ebbsfleet: Hadler, Adebayo-Rowling, Rowan, Kahraman, Taylor, Wood (Dobson 69mins), Paxman, Martin, West (Bingham 60mins), Chapman, Cundle (Eirich 80mins). Subs not used: Mekki, Payne, Holmes, Allen.
Chippenham: Puddy, Jones, Law, Harrison, Parselle, Russe, Lolos, Gunner (Hanks 46mins), Jackson (Zebroski 59mins), Ash, Stearn (Bray 71mins). Subs not used: Shedley, Byrne.
Referee: Daniel Lamport.