A game of few chances saw neither goalkeeper seriously tested, with the visitors missing the chance to climb back above West Brom, who had won 4-0 against Cardiff a day earlier.
The result also kept up Peterborough's impressive home form, with all of their eight points this season coming at thremained e Weston Homes Stadium, although they failed to climb out of the relegation places after failing to score.
In the end, they were relieved to see Dominic Solanke miss two late chances, with the Cherries striker failing to add to his seven goals this season.
The visitors were on a four-match winning run in the league but created little in a competitive first half. Their best chance fell to Manchester City loanee Morgan Rogers who burst into the area, but his shot at the near post was saved by Dai Cornell in the Peterborough goal.
At the other end, Jorge Grant came close to giving Posh the lead, but he was unable to convert Harrison Burrows' right-wing cross on the slide under pressure from former England defender Gary Cahill.
Team-mate Jack Taylor also came close for the home side, but his 35-yard piledriver went narrowly wide.
It was a different story in the second half as the Cherries began to assert their dominance. David Brooks blazed over from inside the area after a short corner routine, before Solanke cut inside onto his right foot but shot straight at Cornell.
Both managers made three substitutions in the hope of injecting a greater attacking threat to their sides, but a winning goal at either end rarely looked likely.
Jonson Clarke-Harris, who is playing while he appeals an FA ban over historic tweets, saw a long-range free-kick easily saved by Bournemouth goalkeeper Mark Travers, which was as good as it got for Posh in the second half.
The home side were, though, indebted to substitute Conor Coventry who blocked a goal-bound shot from Jaidon Anthony after he had been teed up by Solanke.
The former Liverpool and Chelsea striker then had a chance to win it 10 minutes from time as the visitors kept up the pressure on the Peterborough goal, but after pouncing on a loose ball he fired over from inside the area.
Solanke then headed over from a 90th-minute corner as Bournemouth's winning run came to an end, leaving them second in the league behind West Brom on goal difference.