However, Obika came off the bench to hand the Addicks a last-gasp triumph.
However, Charlton had the first real chance of the match when Yann Kermorgant's flick played in Dorian Dervite, whose shot was well saved by Paddy Kenny before Michael Morrison sent the rebound over from close range.
Leeds had a great chance to go in front in the 33rd minute when Green found space before hitting his shot wayward when a pass to Ross McCormack seemed the better option.
Charlton responded through Callum Harriott, but he fired just wide from 25 yards after a driving run at the Leeds defence.
Despite going into the break goalless, Charlton took just two minutes into the second half to go in front as Jackson fired home his 10th goal of the season into the top corner of the net following Andrew Hughes's deflected shot.
Leeds came inches away from equalising in the 62nd minute when Morrison hit the outside of the post after Michael Tonge's effort was bravely headed away by Dervite.
The away side tried their luck at goal again with 20 minutes to go, but Tonge's shot flew over the crossbar.
Leeds did manage to find an equaliser just eight minutes from time when Varney lashed the ball into the top corner.
Chris Solly nearly put the home side back ahead in the 87th minute, but he shot just wide of goal after controlling the ball well in the area.
In the dying moments of the match, Charlton snatched the win after Rhoys Wiggins's cross was met by Obika, who found the back of the net.