Barton Helps Toon Demolish Smogs!
James Marwood scored with a low drive after just four minutes.
Andy Carroll, who played ten minutes on Monday night against Man City, put Newcastle two up with a header.
Richard Smallwood beat Tim Krul to give Boro a chance at 2-1.
But Newcastle's two goal lead was restored when Godsmark's effort was turned past his own goalkeeper by John Johnson.
Godsmark set up Nile Ranger for number four.
Newcastle United: Krul; Edgar (Capt), Kadar (Lough 62), Barton (Inman 80), Tozer, Morris, Godsmark, Doninger, Ranger, Carroll (McCrudden 74), Marwood. Unused subs: Ferguson (gk); Ameobi, McDermott.