The Sabres have won back-to-back games for the third time this season and will try for their first three-game winning streak when they host New Jersey on Saturday.
The shootout goals were the only ones allowed by Theodore after he replaced Florida starter Scott Clemmensen, who was removed following Buffalo's three goals on seven shots in the first period.
Buffalo held a 3-2 lead after 20 minutes with the Sabres' Nathan Gerbe producing his first two goals of the season to start and finish the first-period scoring.
The Sabres maintained that lead until Brian Campbell put a slap shot past Miller with 1:26 to go in regulation.
Miller stopped 38 shots overall.