The Danish striker was out on the edge of the penalty area when he struck a high, speculative lob into the middle with Newcastle goalkeeper Shay Given well off his line.
The ball came down behind Given, who scrambled back too late, landing just outside the goal line and bouncing up into the roof of the net.
"I was surprised it went in. It was a very good effort from Henrik. He tried to hit the target and he made it," said Pedersen's team mate Stelios Giannakopoulos, voted man of the match.
Newcastle manager Bobby Robson said: "They won't kid me it's a brilliant goal. It was a fluke."
The victory ended Bolton's run of five defeats, including the League Cup final.
Defeat prevented fifth-placed Newcastle from getting in front of fourth-placed Liverpool, who also have 45 points, in the tight race for England's fourth Champions League berth next season.
Liverpool were playing at struggling Leicester City later on Sunday while title favourites Arsenal were entertaining champions Manchester United in the game of the day at Highbury.
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