United won 2-1 with goals from Andrew Carroll and James Troisi sending the Magpies into the last 16.
They will play Brentford in the next round.
Newcastle United: Tim Krul, Ross Cowan, Nicky Deverdics, Rob Cavener, Paul Huntington, Lewis Marr, James Troisi, Mark Donninger (Glenn Reay 45), Andrew Carroll, Kazenga Lua Lua (Jonathan Godsmark 66), Dean Critchlow. Subs not used: Michael Terrell, Fraser Forster, Callum Morris.
The big shock was on the south coast as Brighton put out Chelsea. Brighton youth team coach Dean Wilkins was thrilled after his side beat Chelsea 2-1. Joe Gatting and Dan Leach were on target for the young Seagulls.
"I'm really pleased, as we normally fall at such big hurdles - but not this time," ex-Albion midfielder Wilkins told BBC Southern Counties Radio.
Brighton will face Blackburn or Derby in round five.