West Indian great Lara hit 28 runs off an over from South Africa's Robin Peterson in Johannesburg in 2003.
Bailey matched the feat when he took the same tally off paceman Jimmy Anderson in the final over of Australia's second innings on the fourth day of the third Test.
The Tasmanian, in only his third Test, hit three sixes and two fours in the over.
Australian captain Michael Clarke declared on 369 for 6.
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