Alex Kovalev scored a first-period goal, added an empty-netter and notched an assist for the Senators, who snapped an 11-game winless skid.
Michalek's power-play tally 8 minutes into the final frame put Ottawa ahead for good and Regin doubled the advantage 6 minutes later, scoring on 2-on-1 break with Kovalev.
Brian Elliott stopped 15-of-18 shots and Bobby Butler added his first NHL goal and assist for the victors.
Dustin Penner scored twice, Andrew Cogliano added a marker and Nikolai Khabibulin made 20 saves for the Oilers, who lost for the 11th time in 12 home games.
Celebrity Families of 2014 [PHOTOS]