With 6:21 left in the first, Oilers winger Drake Caggiula rifled a shot off the far post in what could have been the go-ahead tally.
In the end, it was the captain who was destined to score the big goal for Edmonton. McDavid came down the ice on a 2-on-1 rush with Patrick Maroon. McDavid shot the puck off the outstretched stick of Kings' defenceman Derek Forort and it flipped over Quick, finding twine. McDavid's 27th goal of the season, scored at 14:44, was assisted by Leon Draisaitl and Andrej Sekera.
A turnover in the slot in front of Talbot led to Jarome Iginla's 12th goal of the season. The veteran scooped the puck up and fired it past the netminder at 17:11 of the first, tying the game at one.
Edmonton scored on their second shot of the second period to take a 2-1 lead. Gryba shot the puck on net and it bounced its way past Quick at 7:03 of the middle frame. Darnell Nurse and Nugent-Hopkins each recorded an assist. The go-ahead goal was only Gryba's second tally of the season.
Nugent-Hopkins had an opportunity to increase the Oilers lead with roughly two minutes remaining in the second. The centre had a breakaway on Quick, but his shot ricocheted off the goalie's glove.
Kassian was thought to have potted the dagger just 2:08 into the third period, but it was waved off by the officials. The winger took a feed from David Desharnais and fired it past Quick, who couldn't get across the net in time. The play came on a delayed penalty, when the puck brushed against a Kings' player's skate and the referee called the goal off. A premature whistle took away a euphoric moment.
As the game wore on, Oilers fans were on the edge of their seats, erupting at every scoring opportunity their team had. They were hungry for that third goal that had so far been denied to them.
With 2:35 left in the game, Draisaitl snapped a shot on net from near the wall and it nearly fell out of Quick's pads, leading to an audible groan from the fans.
As the final minute of play ticked off the clock, the crowd rose to its feet. Talbot kicked away shot after shot from the desperate Kings, until finally it came to an end.
"We're extremely excited and happy for that group in there," said Oilers Head Coach Todd McLellan. "There's a couple here who have been here through a lot of pain and couldn't be more excited for the opportunity that lies ahead of them. Maybe even more importantly, how about our fans? They've been there for 10 years, the rink has been sold out, they've gone through a lot of pain and they've stuck with us. I'm not sure that happens in any other city in the NHL, but it happens here in Edmonton."
With the win, Edmonton (42-25-9) has 93 points on the season and there is an X by their name in the standings. They ended the longest active Stanley Cup Playoff drought, which now belongs to the Carolina Hurricanes (2008-09). The orange and blue continue their pursuit of a divisional crown when they host the San Jose Sharks on Thursday.