It was the Italians' first win of the year and first in 10 internationals since they beat Fiji in November 2013, having lost twice to the Samoans in the last 18 months.
Haimona, making his international debut at the age of 28, gave Italy an early lead with a penalty but Samoa changed ends 10-3 up after flyhalf Tusi Pisi's first penalty and a try through flanker Jack Lam.
Italy hit back soon after the interval with another Haimona penalty followed by a try from flanker Simone Favaro to give them the lead for the first time.
An exchange of penalties put Italy 14-13 ahead before Parisse went over 15 minutes from the end with the conversion putting the home team eight points clear.
Haimona's fourth successful penalty rounded out the scoring. Italy replacement forward Alberto de Marchi's 80th-minute yellow card was too late to matter.
Italy face Argentina in Genoa next Saturday in the second of their November tests.
