In all seriousness, I can't remember a very important Providence / UConn game in years. I can think of huge games with Pitt, Syracuse, Villanova, Miami, St. Johns, Georgetown, Cincinnati... but there's not a "Providence - UConn" moment. When was the last time they played a game in the later rounds of the Big East tournament?
When I think of UConn - Providence games the two that come to mind are Jim Calhoun blowing up over Ryan Gomes (and I couldn't even tell you if Providence or UConn did anything the rest of that year) and the final game of Ollie's first year when Napier was hurt but they won at Gampel vs. Providence.