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.
Alfreton Town 21 Day 02 Law (Mullan - 39' ) 04 Streete 05 Young 12 Franks Booked 07 Brown 14 Hall 22 Church 09 Clayton 11 Arnold (Senior - 56' ) 15 Wilson (Jarman - 80' ) Substitutes 01 Lowson 03 Franklin 17 Mackin 19 Mullan 10 Senior 16 Jarman Carlisle 01 Collin 03 Robson 05 Livesey 19 Ribeiro 25 Michalik 04 McGovern (Curran - 73' ) 11 Thirlwell Booked (Zoko - 62' ) 17 Noble 21 Berrett (Taiwo - 76' ) 09 Loy 14 Miller Booked Substitutes 20 Gillespie 06 Murphy 12 Taiwo 13 Zoko 15 Curran