Pat McCourt and Georgios Samaras hit the woodwork for Celtic before the Greek headed wide from close range.
A wretched night for the home side ended with skipper Stephen McManus sent off for chopping down Andrew Driver.
Celtic have now won just two of their nine home games this season and trudged off to a chorus of boos from disgruntled supporters. The noise was in sharp contrast to the eerie hush at kick off, with Celtic Park only a third full and the top tier of the stadium closed altogether.
But the small band of visiting supporters had something to shout about inside the first minute when Ian Black picked out Nade and the striker's shot beat keeper Lukasz Zaluska, only for defender Andreas Hinkel to clear a couple of yards from goal.
The home side went on to dominate possession but, with Hearts packing men behind the ball, found it difficult to make an impact in the final third of the pitch.
Shaun Maloney did get a glimpse of goal after neat interchange with Zheng Zhi but the Celtic's midfielder's weak shot was easily gathered by Janos Balogh.
A largely drab first half closed with a flurry of activity, with chances at either end. Hearts defender Ismael Bouzid sent a diving header spinning wide from an excellent David Obua delivery and Zheng narrowly missed the target with a shot from the edge of the penalty area.
Chris Killen, playing as the lone striker for Celtic, was foiled by a point-blank save from Balogh once an enterprising run from Aiden McGeady had resulted in a Maloney effort being blocked by a defender.
Hinkel again came to his side's rescue in the first action of the second half when he was on hand to deny Driver, who had knocked the ball past the advancing Zaluska after gathering a headed flick-on from substitute Eggert Jonsson.
Pat McCourt, on as a half time replacement for Maloney, gave the home support a lift when he spun cleverly from his marker on the halfway line and advanced all the way to the edge of the penalty box before fizzing a shot against the crossbar.
On 57 minutes the JamTarts won a penalty when Fox felled Nade as the striker raced after a neat pass from Jonsson. Stewart scuffed a terrible spot-kick straight at Zaluska but the Polish keeper leapt over the ball much to the skipper's delight.
With 20 minutes remaining, McGeady surged through the Hearts ranks and slipped a pass through to Samaras but Balogh was out quickly to block and the prone Celtic substitute could not connect properly as the ball squeezed loose.
Soon after, Samaras stole in behind the Hearts defence and looped a shot over Balogh only to see it rebound off the base of the post. The keeper then held a fierce free kick from Fox before Zaluska had to stretch to gather a deft Nade chip after some neat footwork from the burly forward.
Samaras then contrived to send a free header wide from six yards after McGeady had picked him out with a perfect cross. McGeady bent a free kick over the top after substitute Scott McDonald had been hauled down by Jose Goncalves on the edge of the penalty area and Balogh did well again to block an angled strike from McCourt.
A frustrating night for the home side ended on a sour note with McManus ordered off for a violent hack at Driver. Referee Craig Thompson initially flashed a yellow card but changed his mind after consultation with one of his assistants.