In the second half, late goals from the Addicks' Chris Iwelumo and Hull's Stephen McPhee gave the game a tense finish.
The home side felt they should have been in front midway through the first half as Dean Windass jumped for the ball with keeper Nicky Weaver in the six-yard box.
He headed back across goal giving, Bryan Hughes a simple tap-in, but the referee adjudged Windass to have fouled Weaver as the keeper went down clutching his head.
Charlton took the lead against the run of play on 40 minutes as Andy Reid floated a free-kick into the Hull box which the defence failed to clear, allowing Varney to race in a fire the visitors in front with a close-range finish.
Minutes later both sides were down to ten men as Ian Ashbee fouled Lloyd Sam midway inside the Hull half and the Charlton man retaliated causing the Tigers captain to lash out resulting in a mass brawl.
After the players had been split up, referee Anthony Taylor sent off both Ashbee and Sam for violent conduct.
Charlton were nearly two up on 60 minutes as Danny Mills raced into the right-hand side of the box and rifled a shot against the crossbar from 12 yards.
Iwelumo scored a second for Charlton on 89 minutes as Zhi Zheng collected the ball in the box and squared to the Charlton frontman, who slotted the ball with ease into the back of the Hull net from 12 yards.
McPhee got what turned out to be a consolation for Hull on 90 minutes as Hughes squared the ball to the Tigers striker, who finished the ball neatly from close range to net his first league goal for City.