Joselu’s controversial strike put the Magpies ahead in extra time before Ayoze Perez sealed a third-round-replay victory.
Sean Longstaff and Callum Roberts scored their first Newcastle goals to put the Magpies 2-0 ahead at Ewood Park, with Longstaff netting after just 56 seconds.
But Adam Armstrong and Darragh Lenihan levelled before half time and neither side could find a winner in 90 minutes.
Blackburn’s Bradley Dack missed an excellent chance in the first half of extra time, shooting wide with just Freddie Woodman to beat.
It came just before Joselu put Newcastle ahead again despite the striker being offside when he cashed in after David Raya’s parry.
Perez added a fourth with a fine angled drive just a minute after the re-start in extra time as Newcastle booked a home tie with Watford.
Elsewhere, Stoke were shocked 3-2 by Shrewsbury as Nathan Jones suffered a second- straight defeat.
The League One visitors hit back from 2-0 down with 19 minutes left and will host Wolves.
Tyrese Campbell’s double put Championship Stoke in charge before Shrewsbury scored three times in 10 second-half minutes.
James Bolton, Fejiri Okenabirhie’s penalty and Josh Laurent’s 81st-minute winner completed a miserable night for Jones.
The new boss lost his first game 3-1 at Brentford at the weekend.
Atdhe Nuhiu secured Sheffield Wednesday a fourth-round trip to Chelsea after a 1-0 FA Cup replay win at Luton.
The striker netted just a minute after the re-start at Kenilworth Road to earn the Sky Bet Championship side victory.
The forward scored after being teed up by strike partner Steven Fletcher 58 seconds into the second half.
Cameron Dawson saved well from Luke Berry and Dan Potts to thwart managerless Luton, who lost Jones to Stoke last week.
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