Silfverberg's tally 12:49 into the initial frame triggered the offensive onslaught and he provided a helper on a Guillaume Latrendresse marker during the stretch.
Daniel Alfredsson also scored and later sealed with the victory with an empty-netter after the Lightning had rallied with three goals in the third period.
Eric Gryba found the net as well and Robin Lehner turned aside 29 shots as the Sens improved to 11-2-3 at home.
Tyler Johnson scored twice and Teddy Purcell added a late tally for the Bolts, who dropped a second straight.
Mathieu Garon started in net for Tampa Bay and lasted just 17 minutes before being pulled, yielding three goals on 11 shots.
Cedrick Desjardins stopped 19-of-20 shots the rest of the way.