After Hazard got the ball free, he picked it up and jogged back onto the field.
Hazard and the ball boy apologized to each other after the game, Swansea said in a statement.
He nearly scored a second moments later after Eden Hazard chased down the ball by the byline and fired a cross in toward Ba, but Pantilimon was able to block the effort.
The company pounced when the South Korean flag was shown next to North Korean players on a big screen before an Olympic football game in Glasgow in July and when Chelsea's Eden Hazard clashed with a ball boy in Swansea in January, taking out newspaper ads.
Chelsea's Eden Hazard apologised for kicking a ball boy during his team's Capital One Cup exit to Swansea.
Morgan fell to the ground as Hazard attempted to wrest the ball away from him before the 22-year-old Chelsea midfielder took more drastic action.
CNN: Hazard charged with violent conduct over ball boy incident
Hazard lost patience when the ball boy, 17-year-old Charlie Morgan, was slow to hand the ball back to him after it had gone out for a goal-kick.
CNN: Hazard charged with violent conduct over ball boy incident
The teenager fell to the ground as Hazard attempted to get the ball from him with the Blues midfielder then trying to kick it from under him, but instead he appeared to make contact with the youngster.
BBC: Swansea ball boy Charlie Morgan tweets 'crazy 24 hours'
Hazard ran up to reclaim the ball and the teen fell over, stomach toward the ground and the ball under him.
Cantona's assault was deliberate and intended to harm whereas Hazard was merely trying to get the ball back.
"Hazard is sent off for kicking the ball under a ball boy attempting to smother the ball rather than return it, " Chelsea's tweet read.
Woods had to take off his shoes and socks to play a ball half submerged in the water hazard at the sixth, his 15th, but it paid off.
Chelsea needed to score twice to take the game into extra time and it appeared Hazard lost his patience with Mr Morgan after the ball had gone out of play for a goal-kick.
Chelsea needed to score twice to take the game into extra time and it appeared Hazard lost his patience with the youngster after the ball had gone out of play for a goal kick.
BBC: Swansea ball boy Charlie Morgan tweets 'crazy 24 hours'
"The boy put his whole body onto the ball and I was just trying to kick the ball and I think I kicked the ball and not the boy, " Hazard told the Chelsea website.
They were to drop on the spot he played that shot from, drop in the drop zone, or drop on a line between himself and the hole from where the ball last crossed the margin of the hazard.
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After the game Hazard apologized to the 17-year-old ball boy, who also said sorry to the Chelsea forward, though the Belgian is likely to be banned for a minimum of three games by the English Football Association for lashing out in the way he did.
The ball went out of play and, when a ball boy took his time retrieving it, Hazard went to fetch it himself.
While Hazard has been widely condemned and has apologized to the ball boy, there has also been criticism for the youngster's time wasting antics.
CNN: Hazard charged with violent conduct over ball boy incident
In attempting to work the ball from under his body, TV replays indicated Hazard had made contact with his boot.
CNN: Hazard charged with violent conduct over ball boy incident
With the winded ball boy left on the ground, Foy sent off Hazard, leaving Chelsea with 10 men for the remainder of the 0-0 second leg draw.
CNN: Hazard charged with violent conduct over ball boy incident
With the winded ball-boy left on the ground, Foy sent off Hazard, leaving Chelsea with 10 men for the remainder of the 0-0 second leg draw.
CNN: Hazard charged with violent conduct over ball boy incident
"Chelsea invited the ball boy into the dressing room after the game to shake hands with Hazard and both parties apologized, " Swansea said.
However, if the ball is covered by loose impediments and a player moves it in a hazard, or obstacle area, a penalty of one stroke applies.
If initially Hazard was condemned for actions, he also won plenty of support, with the ball boy -- reported by the British media to be the son of millionaire businessman who sits on the Swansea board -- coming in for plenty of criticism.
Speculation mounted on Saturday morning that Woods might be disqualified for taking a drop in the wrong place after his ball had ricocheted off the flagstick on 15th green and back into the water hazard at the front.
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