Adam Johnson opened the scoring from the penalty spot on 28 minutes after he himself had been upended in the box.
Boro doubled their lead on 41 minutes through Marvin Emnes.
A Lewis Hardman own-goal gave Boro a 3-0 lead before Tony McMahon netted a fourth with 20 minutes remaining in front of just under 6,000 fans at The Balfour Webnet Arena.
The final goal of the game was scored by Johnson whose second of the evening secured a comfortable 5-0 victory against the League Two side.
Darlington 0 Boro 5
Darlington: Kazimierczak; Hardman, Hewitson, Evans (Riley 82), Miller, Ryan, Muirhead, Bayly, Haber (Smith 64), Robinson, Groves (Gray 61). Unused subs: Liversedge, Main, McCready.
Boro: Jones; McMahon, Johnson J (Saiko 67), Williams, Bennett; Owens, Shawky, Walker, Johnson A (Smallwood 80); Emnes (Craddock 59), Porritt (Franks 67). Unused subs: Steele; Corker.