Already last in the NHL in penalty-killing at just under 77 percent, Edmonton surrendered four more power-play goals on eight chances.
Yzerman got Detroit going on the power play 9:36 into the game with his 670th career goal. Darryl Bootland's first in the NHL made it 2-0 in th final minute of the opening period.
Shanahan and Brett Hull sandwiched power-play goals in the second period around Radek Dvorak's fifth of the season. Draper did his damage in the third period, tallying twice, before Steve Thomas capped the scoring with 2:41 remaining.