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With 10 minutes left of the half Dawson almost found a second but missed the target from another Spearing corner.
Posh almost stole an equaliser before the break but Nathaniel Mendez-Laing mi-shit a volley from six yards.
After the break the visitors took a hold of the ball as Bolton began to sit back on their narrow lead. However, Darren Ferguson's side couldn't create any chances of note as the match went into the final 20 minutes.
David N'Gog had the chance to put Bolton two ahead in the 71st minute but sliced his shot wide of the goal.
Marcos Alonso then saw a fierce drive whistle just wide but it was Peterborough who ended on top. They couldn't nick an equaliser though and their chances of survival suffer a blow.
Three points for the Trotters sees them rise five places to 10th while Peterborough remain rockbottom of the Championship.