After a lengthy rain delay, Fish, who was a 2003 finalist, beat the Italian 6-1, 7-5.
Rain then moved in at night to suspend three matches.
James Blake, the top seed, was ahead 3-2 on fellow American Robert Kendrick when play was suspended. The match will be completed Wednesday.
Third-seeded American Sam Querrey was leading Russian Yuri Schukin, 6-1, 3-1, and sixth-seeded American Vincent Spadea was ahead 3-0 on Germany's Denis Gremelmayr when rain suspended both of those matches. They also will be completed Wednesday.
Celebrity Families of 2014 [PHOTOS]