Following a drab first 45 minutes, the Jamtarts went ahead when Jonsson lashed in a diagonal volley.
Nade then added a close range header from Craig Thomson's cross before Killie staged a late rally.
Home skipper Kevin Kyle saw his poor penalty saved by Janos Balogh before Craig Bryson pulled a goal back with a low shot on 89 minutes.
Nade has had to endure much criticism since his move to Tynecastle but the burly striker's second goal in two games proved vital.
Supporters of the home side will, however, look back at Kyle's woeful spot kick and a number of squandered chances.
Balogh was pressed into service on seven minutes when he managed to palm away a Mehdi Taouil corner from under his bar in a crowded six-yard box.
Another corner caused problems for the visitors on 34 minutes and Jamie Hamill lashed a shot high into the net, only for his celebrations to be cut short by the linesman's flag.
Hearts brought on Ian Black in place of Lee Wallace after the interval and had the first action of the second half when Nade shot high over Mark Brown's crossbar.
Kilmarnock immediately responded with a good cross from the left from Garry Hay that 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 Laryea 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 could only to lift the ball into Balogh's hands from the six-yard line.
Hammill then had a one-on-one chance but could not get the better of Balogh, who came out to meet him and diverted the ball out to his left and to safety.
Hearts finally broke the deadlock on 65 minutes, Jonsson finding the bottom left corner with a first-time effort.
Hearts survived a further 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.
Nade was on target with 14 minutes remaining. A corner which he had earned was swung in from Thomson and the French striker 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 Bryson reduced the deficit a minute later, slotting in at the left-hand post after chasing a long ball.