Adelaide's Rory Laird was also successful in overturning his own dangerous tackle ban, but Sydney co-captain Luke Parker wasn't as lucky on a marathon night at the AFL tribunal.
Cerra was charged with rough conduct for his swivelling tackle on Hickey that resulted in the Swans ruckman being slammed back-first into the ground.
Hickey's head whipped back and struck the turf after being brought down, but the Swans big man escaped a concussion.
The nature of Hickey's long hair meant the action of his head hitting the ground was somewhat accentuated and it didn't escape the attention of Cerra's lawyer Peter O'Farrell.
"The hair on this particular player is an unhelpful distraction and we ask you not to be distracted by it," he said.
Lisa Hannon, acting for the AFL, noted the "very fine hairdo", but said there was other evidence that proved how dangerous the tackle was.
"I think if you look at that vision from many angles you won't be for one second distracted by his hair upon seeing the impact as his head hits the ground," she said.
Cerra argued he barely had a grip on Hickey and was off-balance as the Swans ruckman tried to barge through him.
"I was falling. This is a big guy coming through me," Cerra said.
"I didn't pin his arms. I didn't get a grip in the tackle at all. The footage showed I had two fingers around his left tricep and the other arm around his back.
"I did not lift Hickey. I'm not in a position of strength to lift up a guy of that size."
The tribunal panel, led by chairman Jeff Gleeson, found it wasn't a dangerous tackle.
"Cerra only has a light grip on Hickey's arms. They are not truly pinned," Gleeson said.
"Hickey could use one or both of his arms."
The result frees Cerra for Friday night's clash with Melbourne at the MCG.
Laird is available for Adelaide's encounter with Gold Coast on Saturday after successfully arguing he showed enough duty of care in his "slingy-looking'" tackle on Brisbane star Lachie Neale.
"In our view that slowing of momentum, that split-second moment of care, contributed to Neale not being slung into the ground and being exposed to injury," Gleeson said.
Parker will miss Sydney's round-13 clash with the Saints after his one-match ban for a dangerous tackle on Carlton star Sam Walsh was upheld.
The midfielder argued he tried to lower his centre of gravity when laying a tackle on Walsh and showed a level of care for the Blues player.
"I don't think I went in with excessive force once we went to the ground," Parker told the tribunal.
"Once the tackle took place, at no time did I feel he was in a vulnerable position.
"I was dragging my feet across the ground while he had a pretty good stance."
But the tribunal panel disagreed.
The cases involving Fremantle's Jaeger O'Meara (rough conduct for a dangerous tackle) and Lions veteran Dayne Zorko (making contact to the eye region) will be held on Wednesday night.
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