The home team went ahead in the 11th minute when the ball broke loose for Sam Winnall to drill home a low shot from 15 yards.
Izale McLeod was denied by the crossbar before Barnet snatched a deserved equaliser in the 53rd minute as Kabba pounced on a long clearance to fire through the legs of Adam Legzdins.
The striker, who had a spell on loan at Burton from Brentford last season, struck again with brilliant lob in the 64th minute.
And Kabba completed his hat-trick from the penalty spot three minutes later after Sam Deering had been tripped by Scott Malone.
Kabba made it 4-1 10 minutes from the end when he bundled in a Mark Marshall cross at the near post.
Source: PA
Source: PA