Striker Cummins only joined the fray 11 minutes from time but he wasted little time in heading an equaliser to cancel out Joe Garner's first-half penalty for the visitors.
Preston started the brighter with Carlisle keeper Adam Collin having to be alert to stop Scott Laird's inswinging corner creeping straight in.
However, it was the visitors who broke the deadlock on the half-hour. Garner was brought down by Preston keeper Steve Simonsen as he tried to go round him, and the Blues frontman picked himself up to slot home from the penalty spot.
Substitute Akpo Sodje almost made an immediate impact on the hour mark, but North End's top scorer directed a header over the bar.
The Lillywhites were much improved after Sodje's introduction with Nicky Wroe also going close.
And they eventually got the goal their second-half pressure deserved when Cummins' header from a Lee Holmes cross crept inside a post.