James Berrett's 30-yard strike helped Carlisle overcome the stubborn resistance of Ebbsfleet United.
Winger David Symington gave the Cumbrians the lead, finishing coolly from 12 yards out, but Phil Walsh swept home Lanre Azeez's cross to equalise.
Liam Noble's low finish regained the lead and Berrett's fantastic strike was followed up by a Joe Garner header.
Ebbsfleet got a consolation when Joe Howe knocked the ball past keeper Adam Collin into the top left corner.
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Ebbsfleet United boss Liam Daish told BBC Radio Kent:
"The lads put a good show on. We conceded 30 seconds before half-time, got ourselves back, and I thought we could have gone on and won it.
"Some of our players were excellent today and I was really pleased, there was a chance to be giant-killers, and we could have not shown Carlisle as much respect as we did.
"At 1-1 I could only see us winning it. But we maybe weren't aggressive enough."