Eggert Jonsson opened the scoring in the second half at Rugby Park on Saturday and Nade added the visitors’ second 11 minutes later.
Kevin Kyle missed an 87th-minute penalty for Kilmarnock – who dominated the first half and had a goal ruled out for offside – before Craig Bryson scored their consolation a minute later.
Hearts manager Czaba Laszlo made four changes to his side – Jonsson, Dawid Kucharski, Laryea Kingston and Craig Thomson starting in place of Jose Goncalves, David Obua, Ian Black and Gary Glen.
Kyle recovered from a facial injury to play and Mehdi Taouil and Steven Old joined him in the starting XI in place of Manuel Pascali and Gavin Skelton.
In a forgettable first half, Hearts goalkeeper Janos Balogh was pressed into service on seven minutes after Garry Hay’s cross from the byline was diverted into the side netting.
Taouil delivered the corner from the left and the goalkeeper just managed to palm it away from under his bar in a crowded six-yard box.
The home side thought they had broken the deadlock on 34 minutes only for the goal to be ruled out by an offside flag.
Hearts never convincingly cleared their lines following David Fernandez’s corner from the right and the ball finally found Jamie Hamill, who lashed it high into the net, only for his celebrations to be shortlived.
The hosts earned a 28-yard free-kick after Jason Thomson grappled with Fernandez, but Taouil lifted the ball over both the wall and the crossbar.
Hearts brought on Black in place of Lee Wallace after the interval and had the first action of the second half when Nade shot high over Brown’s crossbar.
Kilmarnock immediately responded with a good cross from the left from Hay which Kyle headed just over after arriving at speed to connect.
The visitors had their closest call yet five minutes after the restart with efforts by Jonsson and Kingston, whose acrobatic overhead kick from the penalty spot went wide of the left-hand post.
Hamill and James Fowler both sent chances wide before Kilmarnock missed two golden opportunities to open the scoring just after the hour.
Frazer Wright held his head in his hands on 61 minutes when he had a golden opportunity to open the scoring, but managed only to lift the ball into Balogh’s hands from the six-yard line.
Hammill then ran down the right wing but just as he looked certain to score, Balogh came out to meet him and diverted the ball out to his left and to safety.
Hearts took advantage when they finally broke the deadlock on 65 minutes, Jonsson lashing a diagonal volley into the bottom left corner.
Nade was off target as he tried to double the lead moments later, but Hearts survived a scare when Balogh was unable to get the ball into his arms on the ground in a busy penalty box, but the visitors eventually scrambled clear.
However, Nade made it 2-0 with 14 minutes remaining. A corner which he had earned was swung in from the left by Craig Thomson and Nade thumped home a header at the near post.
Kilmarnock had several attempts to reduce the deficit and were awarded an 87th-minute penalty when Jason Thomson brought down substitute Connor Sammon.
Kyle’s spot kick was saved by Balogh but Craig Bryson reduced the deficit a minute later, slotting in at the left-hand post after chasing a long ball.