Kyle Okposo and Blake Comeau had goals for the Islanders (12-25-4), who have lost 13 straight road games and 15 of their last 17 overall in falling to last place in the NHL standings.
Okposo scored 4 minutes into the game and the Islanders went up 2-0 on a power play when Comeau scored on a wrist shot 2.5 seconds left in the first period.
The Islanders almost went ahead 3-0 when a shot went through goaltender Dwayne Roloson's legs in the crease. But Edmonton took the puck right back into the Islanders zone and scored at 10:50 when Brodziak's shot from the corner deflected off the skate of Islanders defenseman Brendan Witt and past goaltender Joey MacDonald.
Edmonton's fourth line got the job done again just 3 minutes later when Zack Stortini sent a pass from behind the net that was directed in by Strudwick. The goal was reviewed at length as it appeared to have been kicked in, but stood for Strudwick's first of the season.
The Oilers took the lead with 10:02 to play when Marc Pouliot's shot landed in front of the net and seemed to sit there for a while before Cogliano swooped in for his 12th goal.
Notes: It was the only meeting of the season between the teams. ... Pouliot returned after missing two games with a concussion. The same ailment again kept Ales Hensky, Edmonton's leading scorer, out. ... The Islanders were without their leading scorer as Doug Weight was injured in the morning skate in a collision a goalie. ... If the Islanders lose in Calgary on Thursday, they will move within one loss of matching their franchise-worst 15-game road skid, set during 1972-73.