After dropping the opening set to Peru, 21-25, Mercy Moim and Ruth Jepngetich led Kenya into recovery, dominating Peru to take the second set 25-17.
The third set went point-for-point, until the Kenyans pulled away late 25-22.
With the title and a return to Group 2 slipping from their grasp, Peru threw everything at the Africans in the fourth set, and opened up a 3-point lead at the midway point.
The disappointment for Peru was compounded by the site of star player, Angela Leyva, being taken from the arena in a wheelchair after badly injuring her ankle.
After a disappointing 3-0 loss to Peru in the semifinal, the young Colombian team was back to its best as they finished with the bronze medal after beating host nation Australia 3-0 (25-12, 25-22, 25-16) at the Group 3 Final of the FIVB Volleyball World Grand Prix on Sunday.
Colombia coach Eduardo Guillaume said it was hard to get his team focussed for Sunday's match after the disappointment of losing to Peru 24 hours earlier, but he was happy with the application they showed once they got on court.
It was a disappointing finish for the Australians, who were hoping to end their first appearance in their home country for 15 years with a win, and to send off retiring setter Lauren Bertolacci on a positive note.
Colombia was well served by middle blocker, Ivonne Montano, who finished with 12 points, including six blocks.
Rhiannon Tooker led the way for the Australians, finishing with seven points.