Carlisle led at half-time through a David Symington goal but substitute Nathan Elder pulled Fleet level after the break before the Cumbrians ended the visitors' brave resistance with goals from Liam Noble, James Berrett and Joe Garner. Joe Howe rattled in an injury-time consolation for the non-leaguers.
It took Carlisle until first-half injury time before they finally managed to break a stubborn Ebbsfleet defence. The goal came from teenage winger Symington who latched on to Garner's pass and kept his cool to slip the ball past goalkeeper Preston Edwards from 12 yards. Edwards had earlier been the hero, making a series of fine saves to keep the League One side at bay.
The introduction of Elder for Phil Walsh after 56 minutes produced instant dividends for Fleet. The sub found the target with his first touch two minutes later, sweeping home Lanre Azeez's right-wing cross with an assured first-time shot. But Ebbsfleet were level for only three minutes. Noble collected the ball on the edge of the penalty area and drilled home a low shot to restore the home side's advantage.
The goal of the game was supplied by Berrett in the 81st minute. The midfield man controlled the ball 30 yards out and smashed an unstoppable right-foot shot past Edwards into the top corner of the net.
Carlisle put the game to bed in the 87th minute when Garner headed home, although there was still time for Howe to crack a shot past home keeper Adam Collin from 16 yards to give Ebbsfleet the last word.