Puică was born in Iași, Romania and competed at the 1976 Montreal Olympics and the 1980 Moscow Olympics, where she finished seventh in the 1,500 m. In 1978, she placed fourth in the 3,000 m at the European Championships. In March 1982, she won the IAAF World Cross Country Championships. In August, she won a silver medal in the 3,000 m at the European Championships behind Svetlana Ulmasova. She also finished fourth in the 1,500 m final. A month later in September, she broke Mary Decker's world mile record of 4:18.08 with 4:17.44 in Rieti.
Puică missed the 1983 World Championships due to injury, but returned in early 1984 to win her second World Cross Country Championship title. Then in the Summer, she won the inaugural 3,000 m title at the 1984 Los Angeles Olympics, a race remembered more for the collision of Mary Decker and Zola Budd. At those Games, she also won a bronze medal in the 1,500 m behind Italy's Gabriella Dorio and Romanian teammate Doina Melinte.[1]
In July 1986, at the London Grand Prix, she broke Tatyana Kazankina's world 2,000 m record of 5:28.72, with a time of 5:28.69. At the 1986 European Championships in Stuttgart, she won a silver medal in the 3,000 m, behind Olga Bondarenko of the Soviet Union. She was also fifth in the 1,500 m final. 1987 began with her winning a bronze medal in the 3,000 m at the World Indoor Championships in Indianapolis, finishing behind the Soviet pair of Tatyana Samolenko and Bondarenko. Later that year, aged 37, she won a silver medal in the 3000 m at the World Championships in Rome, again behind Samolenko.[2]
Puica competed at her fourth and final Olympic Games in Seoul 1988, where she dropped out of her 3000 m heat with just 200 metres to go.[1]
In 1989, she spoke on Romanian television in support of the revolutionaries fighting against the regime of Nicolae Ceaușescu.
*Distances have varied as follows: Mile (1967–2002), except 1997 and 1999, 2007 and odd numbered years since 2011, 1500 meters 1997, 1999, (2003–6, 2008–2010) and even numbered years since 2010
