Luca Dalmonte's team, just 5-10 and in 13th place in Italy's top flight, opened their EuroChallenge Last 16 campaign with a 76-70 victory over Apoel in Cyprus on Tuesday.
In a contest that was tight from beginning to end, Michael Hicks Taylor made sure Scavolini prevailed with a burst of points down the stretch.
Brandon Heath's three-point play for Apoel knotted the contest at 63-63 with 6:06 remaining.
Taylor then scored six of Scavolini's next eight points to propel them to victory.
He made a lay-up to put them on top and followed that with a dunk.
After a basket by teammate Eric Williams, Taylor caught a pass from Branko Cvetkovic and made a lay-up to extend the lead to 71-63.
The visitors were in command the rest of the way.
Williams poured in 15 points, Dusan Sakota 14 and Taylor 13 for Scavolini.
Heath had 17 points in defeat but was just six of 18 from the floor, including two of four from long range.
Scavolini Pesaro player Dusan Sakota:
"It was an important game. We came here after [having played] a hard game in our championship. It is very difficult to beat APOEL. We played good defense."
APOEL Nicosia coach Christos Stylianidis:
"cavolini are a great team. I am very disappointed with our team. Maybe it is my fault that we made so many mistakes. We cannot play with no discipline. We will try and do our best for the remaining games."
APOEL Nicosia player Gerben Van Dorpe:
"We are disappointed with our game. It was important that we win. We had a lot of turnovers at the end."