Poulsen has struggled to gain a place in the hearts of Juve fans following some average displays and a run of injuries since a move from Sevilla last July.
He made up for it in style in Sicily, and also spared Vincenzo Iaquinta's blushes after the striker was dismissed only moments after heading the opener.
Iaquinta was booked for removing his shirt in celebration but received a second yellow moments later for a foul.
Japanese forward Takayuki Morimoto brought the inconsistent hosts level early in the second half before Poulsen struck.
"It was a very hard match, especially as I've been injured for three months," Poulsen told Rai television. "But we have played as a team."
Injury-hit Juve, who left Alessandro Del Piero and David Trezeguet on the bench, are seven points behind leaders Inter Milan after the champions won 3-0 at Lecce on Saturday. AC Milan are third on 45 after drawing 1-1 with bottom side Reggina.
Fiorentina moved up into fourth on Sunday after Alberto Gilardino scored on the rebound with a minute to go to secure a 1-0 victory over 10-man Lazio.
Lazio coach Delio Rossi is under pressure after a poor run and fan protests but his side did well to manage with a player short for over 70 minutes following Lorenzo De Silvestri's dismissal for two bookings.
In-form AS Roma are joint-fifth with Genoa, a point behind Fiorentina, after beating their rivals 3-0 at home thanks to goals from Cicinho, Mirko Vucinic and Julio Baptista.
