Vale had failed to win any of their previous four home games, but the on-loan Madjo ended that sorry run with some clinical finishing.
A large proportion of Vale fans held up red cards before kick-off as they stepped up efforts to oust chairman Peter Miller and chief executive Perry Deakin, but there were no problems on the pitch with Vale launching a series of attacks before Madjo gave them an eighth-minute lead.
Madjo collected a cross from strike partner Tom Pope and held off the challenge of two defenders before burying a low shot inside Jamie Young’s right-hand post from 12 yards.
Aldershot survived a couple of further scares, but started to play their way into the game as Adam Smith and Luke Guttridge came close to capitalising on some ropey Vale defending. But Madjo settled fraying nerves when he tapped in Vale’s second goal after Young could only parry a shot from Jennison Myrie-Williams in the 48th minute.
And the striker ended the game as a contest on the hour with a left-footed finish from 14 yards after he latched onto a through ball from Pope. The unselfish Pope also played in substitute Sean Rigg to net Vale’s 83rd-minute fourth before Aldershot’s miserable day was completed when Michael Rankine missed an 85th-minute penalty.