The 23-year-old Frenchman saw red on the stroke of half-time with the scoreline still goalless, and the Jambos never recovered from the setback.
In fact Nade had been the visitors' liveliest player in a quiet first period before being sent off for a foul on Fraser Wright.
He had an overhead kick saved by Killie keeper Alan Combe in the 11th minute, while at the other end Danny Invincibile's header was tipped around the post by Anthony Basso.
Michael Stewart's 25-yard free-kick just past the half-hour mark was saved by Combe, but it was Nade's rush of blood to the head that turned the game.
Kilmarnock broke the deadlock in the 55th minute when the outstanding Gary Wales was set up by Colin Nish before striking a half-volley past Basso and into the left-hand corner of the net.
Nish doubled Kilmarnock's advantage with a penalty 16 minutes later following Robbie Neilson's handball.
Hearts assistant head coach Stephen Frail was sent to the stands immediately afterwards for his over-zealous protests.
Willie Gibson made it 3-0 in the 76th minute after Basso's error. The Jambos keeper's terrible free-kick went straight to Gibson who gleefully rolled the ball into an empty net.
Hearts were a well-beaten side but they did score a consolation goal in stoppage-time when Ibrahim Tall headed home Andrew Driver's free-kick, but it was far too little too late for the visitors.