Nikita Rukavytsya opened the scoring for the hosts in the 24th minute, before Shoma Doi leveled matters in the 66th minute.
Then, in the second minute of stoppage time, Kanazaki popped up to secure all three points for the J-League outfit.
The result means the reigning champions are all but out of this year's competition – to progress to the Round of 16 they need to beat Guangzhou Evergrande away in the final group match and hope other results go their way on Match Day Six.
While on the balance of play the Australian side probably deserved more from the match, but their decision to sit back in the second half and defend their 1-0 lead proved to be a mistake.
Following excessive rain in the area and gusting winds around the stadium, the match was always going to be blighted by mistakes and the Rukavytsya's opener came about from one.
Yojiro Takahagi's pass split the Antler's defense, who was slow to react to Rukavytsya's pace and the he made no mistake with the finish.
The Aussies came close to doubling lead just before the half-time break when Romeo Castelen was one-on-one with Kashima's goalkeeper Hitoshi Sogahata, but his finish was wayward and missed the target by a distance.
In the second half, the visitors had the lion's share of possession and eventually their dominance was translated into goals when an inch-perfect through-ball found Doi in space and he made no mistake with his finish past Ante Covic.
Then on the stroke of full-time, with just about the last kick of the match, Mu made up for a series of misses earlier when he latched onto a low cross to send the 5,000-odd traveling fans into raptures.