The visitors began brightly with Lucas Akins and Joss Labadie both trying their luck with long range shots in the opening minutes.
Addicks defender Matt Taylor made a vital headed interception to prevent Enoch Showunmi meeting Dave Raven's cross and Rovers went even closer from the corner when Ian Goodison headed over.
However, Tranmere didn't have long to wait to get their noses in front as Adam McGurk's 33rd-minute 20-yard strike took a deflection off Chris Solly and flew beyond the reach of Charlton goalkeeper Ben Hamer.
The home side were almost level six minutes into the second half in bizarre circumstances when the ball was placed inches wide of his own post by Tranmere captain Ash Taylor. But Charlton were awarded a penalty in the 77th minute when Yann Kermorgant was bundled over by Goodison in the area from Jackson's corner.
There were several protests from the Tranmere players while Jackson waited to take the spot kick but the Charlton skipper kept his composure and made no mistake from 12 yards to maintain the leaders' unbeaten record.