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Matthew Taylor's superb first-half free-kick had given Bolton hope of a precious away win at Turf Moor.
But Nugent headed in a Wade Elliott cross just before the hour mark to salvage a draw which allowed Owen Coyle's men to maintain a three-point cushion between them and the relegation zone.
Burnley were weakened by the absence of injured first-choice centrebacks Steven Caldwell and Clarke Carlisle while Chris Basham came into the Bolton side in place of the suspended Fabrice Muamba.
Bolton started the brighter of the two sides and came frustratingly close to taking the lead when Kevin Davies curled a fine effort inches wide.
Tamir Cohen then tested Brian Jensen with a 25-yard drive before Burnley carved out their first real chance, from which Steven Fletcher should have put them ahead.
Elliott was the architect, robbing Zat Knight of possession before squaring for the Scotland striker, who contrived to drill his shot wide of the post from six yards.
Bolton paid the price of that miss a few minutes later after Andre Bikey, standing in at centreback, was penalised for a foul on Davies.
Taylor stepped up and curled in a superb free-kick to beat Jensen at his near post before sprinting the whole length of the pitch to celebrate with the travelling fans.
Burnley were on the back foot and the home supporters were relieved to see Taylor strike another free-kick from an edge-of-the-box position into the wall before Jensen denied Ivan Klasnic in first-half stoppage time.
The home side looked far shaper after the interval and Kevin McDonald's 50th-minute shot beat Jussi Jaaskelainen only to come back off the underside of the bar.
Bolton might have gone two clear minutes later when Davies flicked on a cross from Chung-Yong Lee, presenting Taylor with a close-range chance that he sent wide of the post.
Fletcher was equally wasteful at the other end, blasting over after being teed up by Nugent before Nugent nodded in Elliott's 56th-minute cross.
Burnley looked the more likely winners from then on but, despite looking increasingly rattled, Bolton held on for a point.
