Maximilian Arnold opened the scoring for Wolfsburg in the 34th minute but Peniel Mlapa equalised after 52 minutes. Ivica Olic put Wolfsburg back in the lead in the 61st minute and Diego finished the match with his strike in the 75th minute.
Wolfsburg increased their undefeated streak to seven matches while snapping their six-match home winless streak and jump to 40 points.
Gladbach picked up their third straight away defeat to remain on 44 points.
The visitors had two good chances early, but Wolfsburg keeper Diego Benaglio stopped Havard Nordtveit's attempt in the second minute and Patrick Herrmann shot wide in the fourth minute.
Wolfsburg went ahead when Diego back-heeled a pass to Arnold, whose left-foot shot was deflected by Roel Brouwers past Gladbach keeper Marc Andre ter Stegen. Arnold has now scored in the last three games for Wolfsburg.
Gladbach nearly equalised in the 52nd minute but Benaglio made a fine save on Nordtveit's shot, which was deflected on its way towards the goal.
But Benaglio could not stop Gladbach just seconds later as Mlapa ran on to a pass from Juan Arango, fended off Wolfsburg defender Naldo and scored the equaliser between the legs of the goalkeeper.
Wolfsburg regained the lead after 61 minutes when Diego sent a through ball to Ivica, who shot through the legs of ter Stegen.
Victory was secured when Olic fed a pass to Diego, who rounded ter Stegen and then hit home from a tight angle in the 75th minute.
Wolfsburg almost made it 4-1 in the 86th minute but Brouwers blocked away Diego's shot.