Liddell's controversial penalty was one of few highlights as Oldham dug in for the points and Bournemouth were unable to break down the stubborn home defence.
The Cherries, who are in the grip of a serious injury crisis, have now won just once in five games.
But this was Oldham's second victory in successive weeks after they beat Gillingham away from home and they are now back in the play-off picture.
Oldham had another boost with Luke Beckett making his first start of the season after recovering from damaged knee ligaments.
And Beckett, on a long-term loan from Sheffield United, almost celebrated with a goal after 16 minutes.
He got on the end of Liddell's corner and saw his header deflected before Steven Foley-Sheridan cleared off the line with Oldham claiming a goal.
Oldham midfield veteran David Eyres shot wide before James Hayter began the second half by shooting straight at home goalkeeper Chris Day.
Beckett was denied by another clearance off the line when Brian Stock managed to get a foot to his goalbound shot.
But Oldham grabbed the winner when Chris Killen was brought down just inside the box by defender Marcus Browning.
Liddell stepped up to beat Gareth Stewart with a spot-kick into the bottom corner and Bournemouth's best chance was soon wasted by Hayter.
Oldham striker Killen blasted off target before James Keene was kept out by a fine save from Day.