Toon Race To Cup Semi!
Forward Baheng was back in action after a 10-month lay-off, having suffered cruciate ligament damage in last season's Northumberland Senior Cup final win over Blyth Spartans at St James's Park.
Mark Doninger and Vuckic had already gave Newcastle a 2-0 first-half lead, and Baheng, a 59th-minute substitute, made his mark with just over a quarter of an hour left on the clock.
James Tavernier and Jonny Godsmark sealed the second-round win in front of a crowd of 354.
Academy director Richard Money was back in the dugout for the game, having been absent for the club's last three second-string fixtures.