Kilman received a total of 27 votes, while Kalsakau got 23 votes.
Kilman, 65, was the deputy PM in Kalsakau's government before being removed in May. At the time Kalsakau had stated that Kilman's dismissal was for "stability of the coalition government".
"Mr speaker first and foremost I want to say a big thank you to the members of parliament and the political parties that supported the change in government. Thank you," he said.
"But thank you even more for standing your ground and for ensuring that democracy prevails in Vanuatu."