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.