The 21-year-old fired in from 20 yards 17 minutes from time to earn back-to-back away wins for Chris Powell's side.
Leon Cort had headed the opener early in the second half as the Tangerines' woes continued.
Blackpool, boosted by the return to the bench of top-scorer Tom Ince following two games out, could have edged in front in the 18th minute when Matt Phillips lined up a shot from 18 yards only to be denied by a block from Charlton centre-half Michael Morrison.
Addicks boss Powell was then forced into an early change as former Dagenham midfielder Danny Green limped off injured to be replaced by Bradley Pritchard before Jamaican striker Ricardo Fuller rattled the Blackpool crossbar midway through the opening period.
French midfielder Salim Kerkar, a summer signing from Rangers, whipped in a low corner from the right which was met by the stooping figure off Fuller but his header bounced down off the underside of the bar and away.
In an absorbing opening period, Ian Holloway's man responded to nearly going behind with two efforts of their own.
Striker Gary Taylor-Fletcher attempted an audacious chip from 40 yards which landed on the roof of Ben Hamer's goal before Phillips forced the Addicks goalkeeper to save low down to his left with a drilled strike.
Danger man Fuller threatened again on the stroke of half-time when his 12-yard drive was tipped around a post by Matt Gilks.
The south Londoners continued to cause Blackpool problems from set-pieces and broke the deadlock four minutes after the interval.
Dale Stephens swung a corner over from the left and centre-back Cort rose unchallenged to send a thumping header past Gilks for his second goal of the season.
Home manager Holloway reacted to the setback by introducing Ince in place of Portuguese midfielder Tiago Gomes but his usually free-scoring side were struggling to create chances.
The next goal was always likely to prove decisive and it was Charlton who extended their lead 17 minutes from time. Left-back Solly seized on the ball after Stephens' shot had deflected into his path to strike an unstoppable drive into the top right-hand corner with the outside of his right foot.
Substitute Nouha Dicko, who was thrown on with fellow striker Kevin Phillips prior to Solly's strike, came close to a consolation for the home side but his right-foot volley flew wide of the right-hand upright.
And Athletic held out to record a second clean sheet of the season and a first win at Bloomfield Road since 1981.