King, a senior, made it 15 straight games with each thanks to a 35-yard scoring run in the second quarter of a 38-31 loss to host Tulane.
That breaks a tie with Tim Tebow for the longest streak in FBS history. No other player has an active streak longer than three games.
Earlier Thursday, King had completed touchdown passes of 75 and 28 yards. For the game, he went 16-for-33 for 229 yards with two touchdowns and rushed for 116 yards and a touchdown on 17 carries.
King's streak started at the beginning of the 2018 season. After Thursday's loss, he has thrown for 3,645 yards and 42 touchdowns to go along with 986 rushing yards and 20 rushing touchdowns during the streak.
Tebow, during his 14-game streak with the Florida Gators, threw for 3,287 yards and 33 touchdowns to go with 934 rushing yards and 24 rushing scores.
ESPN Stats & Information contributed to this report.