Goals from Florian Lejeune and Allan Saint-Maximin gave Steve Bruce's side their second victory over Championship opposition in just four days following Tuesday's 3-2 win against Middlesbrough at the Magpies' training ground in Benton.
Lejeune opened the scoring in the first half, heading home Jonjo Shelvey's accurate cross from a free-kick.
And Saint-Maximin doubled the lead just before the break, picking up a loose ball in the box and side-footing it beyond Tigers goalkeeper George Long.
The Magpies return to Premier League action against Sheffield United at St. James' Park on Sunday 21st June (kick-off 2pm BST).
While supporters will not be able to attend, the match will be broadcast live on Sky Sports.
For the latest coronavirus guidance, please visit gov.uk/coronavirus.
Newcastle United: Martin Dúbravka (Karl Darlow 60), Javier Manquillo, Florian Lejeune (Fabian Schär 36), Federico Fernández, Danny Rose (Andy Carroll 46), DeAndre Yedlin, Jonjo Shelvey (Isaac Hayden 64), Nabil Bentaleb (Emil Krafth 72), Allan Saint-Maximin (Matt Ritchie 64), Miguel Almíron (Valentino Lazaro 64), Joelinton (Yoshinori Muto 64).