Ottawa has been eliminated in the playoffs each of the last three seasons by the Toronto Maple Leafs while Joseph usually played the starring role.
In his first appearance against the Senators for his new team, Joseph surrendered five goals on 34 shots. He fell to 13-14-1 lifetime against Ottawa in the regular season.
Smyth scored 45 seconds into the second period to snap a 1-1 tie and Van Allen tallied just over 13 minutes later for the Senators, who stopped a four-game winless streak. Ottawa also snapped a four-game skid against Detroit.