Carlisle hit four goals in 20 first-half minutes to ease into the FA Cup second round at Alfreton's expense.
After early Alfreton pressure, the visitors grabbed the lead when Lee Miller fired in from close range.
Christian Ribeiro crossed for Rory Loy to notch an overhead kick, and James Berrett's strike and Liam Noble's header made it 4-0 before the break.
The Reds had a chance to get back into the game but Chris Senior saw his penalty come back off the crossbar.
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Alfreton Town manager Nicky Law told BBC Radio Derby:
"Other than a mad 20 minutes, we've matched them.
"We came out in the second half and had a penalty miss and we had another good chance just after that. At 4-2, who knows?
"Unfortunately it was not to be and we've been beaten by the better team today because those 20 minutes cost us.