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Striker Darren McQueen and substitute Stuart Lewis both scores twice as Fleet went nap on Saturday.
A goalless first half at Stonebridge Road was dominated by the hosts and they got their rewards after the break against Ryman League AFC Sudbury.
It puts Daryl McMahon's men into the hat for the third qualifying round draw on Monday.
Fleet made three changes from the team that won 3-0 at Bishop's Stortford in midweek with keeper Jonathan Miles, Reiss Greenidge and Darren McQueen all coming into the side.
Fleet had the best of the early chances as the pace of McQueen and the inventive Sam Deering gave Sudbury plenty to ponder.
They should have gone ahead on 14 minutes but McQueen opted not to give the unmarked Danny Kedwell a simple tap-in and instead his low shot was beaten away by keeper Marcus Garnham.
Ryan Auger's free-kick was beaten away at the other end by Miles before Fleet ended the half well on top.
Kedwell set-up Deering, whose low drive was turned behind, the resulting corner seeing Kedwell head over at the near post.
Then Sean Shields beat a couple of defenders inside the area but again found Garnham in his way, the keeper then keeping out Deering.
The Fleet were indebted to Shields in first-half stoppage time, however, when James Baker's header from a right-wing corner was cleared off the line.
It took the lead just eight minutes of the second half to go ahead. Garnham failed to cut out a deep cross and Kedwell gambled to keep the ball in, his touch setting up McQueen to score from close range.
Just 60 seconds earlier, McQueen should have put the Fleet ahead but he failed to get his shot away after being sent clean through and Garnham was out to save. McQueen made no mistake second time around.
Deering again went close from distance before McQueen's pace and endeavour earned him a second goal on 65 minutes. Indecision between Garnham and Ryan Henshaw allowed McQueen to nip in and the striker needed no second invitation to hook home his second of the afternoon.
McQueen then turned provider for Anthony Cook, but his right-foot chip landed just wide of the upright.
Within a minute of Fleet replacing two-goal McQueen, they added a third when Kedwell crossed for Jack Powell to tuck home from close range.
Substitute Lewis then scored twice in two minutes as Sudbury fell apart in the last five minutes. He drove into the box before taking advantage of a fortunate deflection to add a fourth on 86 minutes.
Then within 60 seconds, Lewis had time and space to pick his spot on the edge of the area and fire low beyond the exposed Garnham.
Ebbsfleet: Miles, Cook, Shields, Greenidge, McCoy, Clark, Rance (Lewis 46mins), Deering (Kissock 66mins), Kedwell, McQueen (Bubb 80mins), Powell. Subs not used: Ashmore, Sheringham, Connors, Boulding. Attendance: 855.