Atalanta looked the more dangerous of the two sides in the early stages, and the hosts were inches away from taking the lead when Germain Denis headed just past the post from only a few yards out.
Parma improved as the first half progressed, but their best opportunity was wasted when Massimo Coda sent his wayward effort over the crossbar after being gifted space on the edge of the box.
Another spell of Atalanta pressure arrived after the break as Maximiliano Moralez became the latest player to threaten the Parma defence with a curled shot which drifted wide of the target.
Atalanta's frustration continued to grow, and it appeared as though their bid to find a winning goal would end in disappointment when Daniele Baselli fired a great chance over the crossbar.
However, the home fans were finally given a reason to celebrate in the final minute of normal time when Antonio Mirante pushed a powerful strike from Luca Cigarini straight to Boakye, who converted from close range to secure all three points and inflict a fourth straight loss on Parma.