Kohli reached the 7000-run mark with a glance to the boundary at fine leg from the bowling of James Faulkner.
Kohli passed 7,000 runs in his 161st ODI innings, four fewer than the 165 that South African AB de Villiers took to reach the same milestone.
However, Kohli is unlikely to hold the record for long, with South Africa's Hashim Amla currently on 6,008 runs from 121 innings.
Kohli held the record for the fastest player to 5,000 and 6,000 runs, only for Amla to break both those marks.