Melinte was born in Bacău, Romania. She competed as Doina Besliu at the 1980 Moscow Olympics and reached the semi-finals of the 800 metres. In 1982, now competing as Doina Melinte, she was the fastest woman in the world at 800 metres but only finished sixth in the final of that years European Championships in Athens. She also finished sixth in the 800 m final at the 1983 World Championships in Helsinki.
At her third Olympic Games in Seoul 1988, she finished a disappointing ninth in the 1500 m final won by her Romanian team-mate Paula Ivan. In 1989, she successfully defended her 1500 m World Indoor title in Budapest, winning in a championship record of 4:04.79. In February 1990, she broke the world indoor mile record with 4:17.14 in East Rutherford. The record (as of 2014) still stands. A month later, she won her third European Indoor title over 1500m in Glasgow. A medal favourite for the 1990 European Championships in Split, she could only finish sixth in the 1500 m final. In 1991, she was fourth in the 1500 m finals at both the World Indoor Championships in Seville and the World Championships in Tokyo.
Melinte concluded her international career at the 1992 Barcelona Olympics, where she dropped out of the 1500 m final with 300 m to go.