Kohli, captain of the Royal Challengers Bangalore, has racked up 752 runs in 12 matches so far this year including three centuries and five 50s.
Kohli’s 75-run blitz on Monday kept the Challengers’ play-off hopes alive after they crushed the Kolkata Knight Riders by nine wickets.
The Indian batsman overtakes the powerful Gayle, who scored 733 runs in 15 matches in 2012, while Australia’s Mike Hussey tallied the same figure in 17 games in 2013.
Kohli, who batted with an injured finger, stitched together a 115-run unbeaten stand with AB de Villiers (59).
Their partnership comes just two days after they recorded the highest partnership (229) in Twenty20 cricket history during the Challengers’ match against the Gujarat Lions.
Team-mate Gayle, who also found form at Eden Gardens with a 31-ball 49, paid credit to the in-form duo.
“Those two guys are playing like Batman and Superman. They are in the form of their life,” said the Jamaican.