Draisaitl extended it to 3-0 at 8:42 of the second period, becoming the fastest Oilers player to score 40 goals (61 games) since Jimmy Carson in 1988-89 (55 games).
Darnell Nurse made it 4-0 at 13:42 when he swept in a loose puck in the left circle.
"When you're playing teams that are not really in the race and they're playing loose and they've got some good young speed [and] talent, it can definitely be tough to shut it right down like that," Barrie said. "You don't just want to sit back either. I think the Detroit game (7-5 win on Tuesday) was a good lesson for us. It was nice to learn from that and put it to the test, and I thought we were great all the way through."
Olofsson scored at 3:21 of the third period to make it 4-1, one-timing a cross-ice pass from Rasmus Asplund.
Devin Shore scored on a shorthanded breakaway at 5:58 to make it 5-1.
"I thought we got contributions from everybody, all four lines, three 'D' pairs, and Mike Smith was excellent," Oilers coach Jay Woodcroft said. "The penalty kill was good, we got a shorthanded goal, we got a power-play goal, all facets of the game seem to be firing on all cylinders, and because we had everybody going, we were able to spread out the minutes nicely tonight."