Jonson Clarke-Harris struck his 31st goal of the season early in the game before Josef Bursik saved a penalty just after the half hour mark.
Posh defended superbly as Charlton failed to create any clearcut opportunities in the second half..
RATINGS KEY: 10-Brilliant, 9-Outstanding, 8-Very Good, 7-Good, 6-Okay, 5-Poor, 4-Dreadful.
JOSEF BURSIK: What a penalty save from the on-loan 'keeper and what a cool customer he is when handling or kicking. An excellent recruit 8.5.
NATHAN THOMPSON: Didn't play with his usual panache on the ball and he struggled defensively against winger Liam Miller. Taken off with 20 minutes to go 6.
DAN BUTLER: A superb defensive display from the left-back who also used the ball wisely to help Posh break out 8.
FRANKIE KENT: Unlucky to concede a penalty, but that was the only time he was less than foot perfect. Terrific when the ball came into the Posh penalty area and executed some well-timed tackles. Outstanding 9.