They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
It also marked the first 300-run stand in women's cricket, eclipsing the 268-run partnership between England openers Caroline Atkins and Sarah Taylor against South Africa in 2008.
The 19-year-old Sharma hammered 24 boundaries and two sixes in her 160-ball innings to score 188, the second-highest individual score behind Australian Belinda Clark's unbeaten 229 against Denmark 10 years ago.
India went on to score 358 for two before skittling Ireland for 109 to record a 249-run victory in a quadrangular series that also features hosts South Africa and Zimbabwe.