Strome put Edmonton up 2-1 at 18:51, finishing off a cross-crease pass from Draisaitl for the 10,000th goal in Oilers history.
"It was an interesting start because we had that early power play and didn't get anything with it," Oilers coach Todd McLellan said. "Then they score, and the penalty kill has been our nemesis and I thought we sagged a little bit there. But I thought a lot of good things were being said on our bench to overcome it to get our own non-power-play goal -- it was a second after -- and that got us our momentum back and we seem to establish it from there and play well."
Nugent-Hopkins gave the Oilers a 3-1 lead at 6:36 of the second period when his centering pass for Drake Caggiula went in off Pavelski's stick.
Hertl scored at 8:32 to cut the Edmonton lead to 3-2 on a shot from the slot.
Maroon scored at 8:23 of the third period to give the Oilers a 4-2 lead, but Sorensen made it 4-3 at 11:58, avoiding a poke check from Talbot before scoring on his backhand.
Strome scored into an empty net with 7.6 seconds left to make it 5-3.
"Winning at home was important," Strome said. "We were resilient. We have gotten the ship slowly going in the right direction the last eight or nine games. We have to keep it going. Obviously, the divisional games are very important. We have a lot of those in the second half, and this is a good start."