A chaotic season marked by four managerial changes had left the Sicilians stranded in the bottom three without a win in 15 games, but that would soon change against European hopefuls Roma.
Goals from Josip Ilicic and Fabrizio Miccoli earned a shock 2-0 victory over the capital club to draw Palermo within three points of safety, with victory at the Marassi now promising a possible share of 17th place.
Zamparini told La Repubblica: "The miracle happened. I saw a Palermo side charged by the desire and conviction to succeed.
"Our year has been cursed until now but now we have rekindled the flame and there is a trickle of hope.
"I don't think the fight will just be between Siena, Genoa and ourselves but the teams on 34 or 35 points could get sucked in if they go three or four games without winning.
"We have what it takes to climb out of it."
Goalkeeper Stefano Sorrentino could be missed, though, should he fail to recover from a muscle complaint with striker Abel Hernandez and midfielder Andrea Mantovani still struggling for fitness.
Defender Ezequiel Munoz serves a one-match suspension alongside Samp midfielder Andrea Poli.
The Ligurians enjoy a healthy 10-point gap above the relegation zone but Wednesday night's 2-0 home defeat to Inter Milan put things in perspective for head coach Delio Rossi.
He said: "If you lose because of isolated incidents then it means you have not been paying proper attention.
"We are not yet in a position to stop worrying about the league table.
"This was an important game but there are certain matches from which you definitely need to take a result, and our game against Palermo is one of them."
The Sicilians, however, have a good recent record over Samp, claiming three straight wins and avoiding defeat since May 2008 - eight meetings ago.