The visitors twice went ahead, through Antoni Sarcevic and Jamille Matt, but Nardiello's goals ensured the Shakers remained unbeaten at home under David Flitcroft.
Fleetwood found plenty of space in the opening stages and Brian Jensen made a sharp save to keep out Nathan Pond's header from a Josh Morris corner.
Bury only woke up following a tactical switch and substitute Tom Soares forced Chris Maxwell into a superb, full-length save to keep out his effort.
But the visitors went ahead in the 41st minute when Bury failed to clear a Morris cross and Sarcevic fired home at the far post.
The equaliser was not long in coming though as Nardiello flicked Danny Mayor's cross past Maxwell at the start of the second half.
Fleetwood restored their advantage in the 57th minute, with Matt reacting quickest after Jensen had denied Jon Parkin.
But Bury were level again four minutes later. Nardiello netted from the penalty spot after Charlie Taylor had fouled him inside the box.
Jean-Louis Akpa Akpro produced a moment of brilliance but could not clinch victory, his shot was blocked well by Maxwell.