The Thundering Herd (4-2) led 77-67 with 2:36 remaining, but a quick 9-2 run pulled the Golden Panthers within 3, 79-76, with 1:14 left to play.
Then seven free throws and a layup from Kane down the stretch sealed the win for Marshall.
FIU shot 14 for 23 from the floor (60.9 percent) in the first half but trailed 43-36 at the break. Kane scored 13 in the first and Johnson added 10 as the Thundering Herd maintained a slight advantage.
Marshall led by as many as 13, 53-40, thanks to three free throws from Dago Pena with 17:08 to play in the second half.