The Magpies progressed to face Watford after Joselu struck just before half-time in the additional period - an effort it appeared should have been disallowed for offside - and substitute Perez added a powerful finish just after the interval.
Newcastle had gone 2-0 up early on via two 21-year-olds scoring their first goals for the club, Sean Longstaff netting with a deflected shot in the opening minute and Callum Roberts then marking his full debut with a 22nd-minute volley.
Blackburn responded impressively, with former Newcastle striker Adam Armstrong pulling a goal back in the 33rd minute and Darragh Lenihan levelling with a header in first-half stoppage time.
Isaac Hayden - brought on when half-time substitute Jamaal Lascelles went off injured just before the hour mark - went close to putting the visitors back in front in the second half of normal time when his header hit the post.
Newcastle, who had been winless in their previous six games in all competitions, will host the Hornets on January 26.