The Oilers also won the first two games between the provincial rivals this season. The Battle of Alberta series will wrap Jan. 21 at Calgary.
"We were nowhere close at the start (of the season) there," captain Mark Giordano said. "We gave them breakaway after breakaway in those first few games. Tonight we were aware of getting above them. They're a tough team to play against. They play with a lot of speed. You could see some confidence in some of their players that are really rolling.
"We did a good job. The shootout sucks.
"It feels like a loss, but it shouldn't if you really think about it."
Draisaitl and Mark Letestu scored in the opening two rounds of the shootout, and Talbot stopped both Monahan and Johnny Gaudreau to clinch the win.
"We got out of (overtime) unscathed but I couldn't come up with a save in the shootout and we couldn't get a goal, either," Elliott said.
Elliott's heroics in overtime forced the game to a shootout.
He stopped Jordan Eberle's redirect on a setup by Oscar Klefbom at 4:08, and, after Gaudreau hit the post, Maroon's deke with two seconds remaining in OT.
"Huge saves in the overtime period, which helped us," Gulutzan said. "It got us to a shootout, which you all know is anybody's ball-game. Some of the saves he made, especially in that overtime, were big saves for us."
Elliott made seven first-period saves; Talbot made five, including two glove saves on chances off the stick of Monahan. Monahan one-timed a setup by TJ Brodie on a 3-on-1 that he snagged at 8:19. Talbot flashed the glove again on Gaudreau's slap-pass into the slot on the power play that Monahan redirected at 14:12.
Maroon put the Oilers up 1-0 with a power play goal at 16:24 of the second period, but Monahan replied 26 seconds later with his second goal in as many games after going 11 straight without scoring. Talbot made the initial save on Monahan's drive to the net, but the 22-year-old netted his 12th goal of the season by following up with his rebound.