Goals from Emmanuel Ledesma, Merouane Zemmama and Richard Smallwood gave Boro the victory.
North End took Championship scalps from Huddersfield and Crystal Palace to reach this stage of the competition, but the challenge of an impressive Middlesbrough proved too much as a trio of defensive errors put them out at the third round for the fourth year running.
Both Ledesma and Andrew Halliday claimed to have scored Boro’s 13th-minute opener, with the Argentinian’s inswinging corner striking the far post and rolling over the line with Halliday making sure by bundling in.
Five minutes later, Preston allowed Zemmama far too much time to shoot into the bottom corner from 25 yards five minutes later, but the hosts pulled one back through Jack King’s smart finish on 40 minutes.
Smallwood capped a comfortable win for Boro on 61 minutes, pouncing on the loose ball after Preston defender Paul Huntington headed Zemmama’s cross back to Steve Simonsen, too powerfully for the keeper to hold, as the visitors eased to victory.