Wingti is a member of the Jika Tribe of the Western Highlands province. While doing his final year in Economics at the University of Papua New Guinea, he stood for election in 1977, winning to become a member of the Hagen Open in the country's National Parliament. In 1985, as leader of the People's Democratic Movement (which had broken away from the Pangu Party), he became the youngest Prime Minister in the Commonwealth when Michael Somare lost a confidence vote. Julius Chan, who would himself become Prime Minister, served as his deputy.
In 1987 Wingti returned to power with a slender majority of three votes. He announced a more independent foreign policy, attempting to enhance relations with the Soviet Union, U.S., Japan and China. He lost a motion of confidence in 1988 with changes in the shifting coalition and was succeeded by Rabbie Namaliu, the new leader of the Pangu Party, but Wingti returned for a further two-year stint in 1992. His second term was marked by an escalation of unrest in Bougainville and he was ousted by Julius Chan in August 1994. Wingti continued to represent the Western Highlands in the National Parliament of Papua New Guinea, although he switched from the local Hagen constituency to the provincial-level electorate in 1995.
Wingti served as the governor of Western Highlands Province from 1995 to 1997, when he was defeated for re-election by Father Robert Lak. He returned to parliament in 2002, defeating Lak to regain his seat and the governorship. He subsequently won back the leadership of the People's Democratic Movement from Mekere Morauta, who had taken over after his defeat, in 2007. However, he was defeated in his bid for re-election at the 2007 election, losing to former student activist Tom Olga, largely as a result of the new preferential voting system. Wingti, along with fellow former Prime Minister Rabbie Namaliu, were the most high-profile losers of the election. Additionally, Wingti lost the governorship of West Highlands Province to Olga. The PDM also suffered a major defeat in the election, losing several seats.