On july 1, 1962 The White Sox drop Cleveland to 3rd place while winning a pair, 5 – 4 and 7 – 6. In the second game, they also set a major-league record with three run-scoring sacrifice flies (by Juan Pizarro, Nellie Fox and Al Smith) in the 5th inning when they score six runs. Indian RF Gene Green makes the first putout of the 6th inning, but then muffs two other fly balls, both of which are credited as sacrifice flies, the scorer assuming the runners on 3rd could have scored anyway.

Source
Baseball Reference July 1