It was the first of three home ties in a row as fellow Premier League club Chelsea travelled north to Tyneside in round four.
A four-minute first-half spell settled the encounter in the hosts’ favour, Alexander Isak’s opener quickly followed by an Axel Disasi own goal to secure a 2-0 victory.
Brentford were the next to try to stop Howe’s charges but festive cheer came from the Toon Army courtesy of a 3-1 result a week before Christmas.
Sandro Tonali struck twice before the interval to put Newcastle in charge and their advantage was later enhanced by Schar, leaving Yoane Wissa’s stoppage-time goal as little consolation for the Bees.
North was pitted against south on the other side of the semi-final draw too, with the Magpies paired against Arsenal and sent to Emirates Stadium for leg one.
There, they took a big step towards Wembley with unanswered strikes either side of half-time, Isak again breaking the deadlock and Anthony Gordon adding a second.