Our Cornwall-based hosts took the lead just four minutes in. Luke Jephcott converted a penalty, before teeing up Dominic Johnson-Fisher to double their advantage with a sweeping first-time hit into the top corner.
City responded almost immediately through Hugo de Lisle, whose goal halved the deficit, though Jephcott soon got in on the action again; his curling free-kick making it 3-1 with under half an hour played.
Four minutes into the second half, Johnson-Fisher also completed his brace and that's how it stayed, to leave Leicester in sixth, on one point from our opening two matches in Group D, while Truro sit top with a 100 per cent record.
Next up in the competition, on Tuesday 13 October, we face another National League side, Woking, at Laithwaite Community Stadium (7:45pm kick-off).
Before then, attention turns back to Premier League 2 and our meeting with Brighton & Hove Albion this Friday - a 7pm kick-off at AMEX Elite Football Performance Centre.
The details
City: Marson, Donnelly, Toko (Szembell 87'), Gray, Daniels (Khela 60'), Diallo, Lawrence, Anugo (Aideed 70'), Hutchinson, de Lisle (Manyumba 87'), King (Corden 60').
Sub not used: Stretton.
Goal: de Lisle 22'
All times BST.