They said a first count found Sharon had won by 63% to 37% in a ballot that could avert a snap election and pave the way for a broad coalition that would allow him to push through his Gaza withdrawal plan.
Sharon has proposed removing all 21 Jewish settlements from Gaza and four from the West Bank, reversing decades of support for building and expanding settlements.
All settlements are illegal under international law, and Palestinians say Sharon plans to pull out of Gaza so he can consolidate control over the West Bank.
Many members of his Likud Party have rejected his new policy, and his government has lost its majority in parliament.
Likud already voted in August against inviting Labour to join the government.
But after Sharon fired a key coalition partner for voting against his budget on 1 December, his coalition became more tenuous than ever.
He then warned that the choice now was Labour or elections.