The Magpies, backed by over 6,500 away supporters this evening, conceded in the 14th minute as Abraham latched onto Douglas Luiz's free-kick inside the box before firing the ball past Aaron Ramsdale.
The striker was situated in an offside position following Luiz's pass but, with no VAR in place for the cup tie, the goal stood.
Eddie Howe made six changes to his starting XI which claimed a 2-1 away win against Tottenham Hotspur in the Premier League on Tuesday night.
Aaron Ramsdale, Lewis Hall, Sandro Tonali, William Osula, Jacob Murphy and Nick Woltemade all come in for Nick Pope, Sven Botman, Bruno Guimarães, Anthony Gordon, Anthony Elanga and Joe Willock.
United booked their place in the fourth round after beating AFC Bournemouth via penalties after last month's thrilling 3-3 draw at St. James' Park.
Newcastle travelled to the second city for last season's FA Cup fourth round tie, coming from behind to claim a 3-2 win against Birmingham City.
**Newcastle United:** Aaron Ramsdale, Kieran Trippier (c), Lewis Hall, Sandro Tonali, Harvey Barnes, Malick Thiaw, William Osula, Jacob Murphy, Nick Woltemade, Dan Burn, Jacob Ramsey.
**Subs not used:** Nick Pope, John Ruddy, Anthony Gordon, Anthony Elanga, Joe Willock, Alex Murphy, Leo Shahar, Sean Neave, Seung-soo Park.