Connolly achieved the feat during Punjab Kings' clash against Royal Challengers Bengaluru in Dharamsala on Sunday, a contest played under bowler-friendly conditions.
Despite the challenging surface, the left-hander produced a brisk 38 off 27 deliveries, striking two sixes in the process.
Those maximums carried him to 32 sixes in his debut IPL campaign, allowing him to surpass former Sri Lankan great Sanath Jayasuriya for the most sixes hit in a maiden IPL season.
Jayasuriya had previously held the record since the inaugural 2008 edition, when he smashed 31 sixes for Mumbai Indians.
Connolly has emerged as one of Punjab Kings' standout performers this season, particularly through his productive partnership with Priyansh Arya, which has become one of the franchise's biggest positives during the campaign.
The Australian has drawn praise for both his clean shot-making and his ability to adjust to varying match situations and conditions.
The Western Australia batter has already registered a century this season and has compiled 473 runs in 13 matches at an average of 47.30 and a strike rate of 162.4.
Away from the IPL, Connolly represents Western Australia in the Sheffield Shield and Perth Scorchers in the Big Bash League. He has also broken into the Australian national side across all three formats, featuring in one Test, eight ODIs and 11 T20 internationals.