The victory was just the Avalanche's fourth in 12 home games and their second win in the past seven games overall.
"It was a real important win for our club," Avalanche coach Joe Sacco said. "It's going to hopefully boost our confidence right now. Being able to score five, especially at home … it was a good period. We showed some resiliency in our game. That was good to see."
It was a difficult defeat for the Oilers, who were looking to pull within one point of Northwest Division-leading Minnesota. Not only did they squander the third-period lead, the Oilers lost forward Taylor Hall, the first overall pick in the 2010 NHL Draft, to a left shoulder injury in the first period on a big hit by Ryan Wilson.
Hall will be re-examined by team doctors when the Oilers return to Edmonton. They next play Nashville at home on Monday.
"We'll see how bad he is," Oilers coach Tom Renney said. "He's a got a bit of a shoulder injury. We'll see what the MRI tells us. Step back from the ledge, first of all. Just relax and see what the MRI and the medical staff tell us."
Renney said his team tired in the third period. Saturday's game completed a four-game trip and the Oilers played Friday in Minnesota.
"We took some penalties," he said. "That didn't help, obviously. I think maybe fatigue caught up to us, probably cost us the game at the end of the night. We were on fumes in the third period."
O'Brien and Elliott, who made his NHL debut, scored 1:57 apart to give the Avalanche a 3-2 lead before Hejda found the back of goalie Devan Dubnyk's net with 3:40 to play after David Jones kept the puck alive in the Oilers end by outracing an Edmonton defender to negate a potential icing.
Elliott, summoned from Lake Erie in the American Hockey League Friday when Erik Johnson was placed on injured reserve with a groin ailment, broke a 2-2 tie at 8:03. Ryan O'Reilly won a faceoff in the left circle and drew the puck back to Elliott, who skated to his right and put a screen shot that eluded Dubnyk to the stick side.
"Just pure joy and excitement," said Elliott, who became the first Avalanche defenseman to score a game-winning goal in his first NHL game. "It is something special to score my first goal, let alone it being my first game. It is nice to get that one out of the way."
Elliott, 20, was the Western Hockey League's Defenseman of the Year last season when he had 31 goals and 81 points in 71 games for the Saskatoon Blades, so his best assets are skating, shooting and passing.
"I think it went really good," he said. "It is nice to get that win for sure. I was pretty anxious coming in here, but it is definitely nice to get this first (game) under my belt. Hopefully, there is a lot more to come in my career. I tried to calm the nerves a little bit and just came in here and got ready to play."
Moments earlier, Elliott broke up a 2-on-1 Oilers' rush, a play that impressed Sacco as much as the goal. Elliott, a second-round pick (No. 49) in the 2009 NHL Draft, also had two shots on goal and was a plus-1 in 19:36 of ice time.
"He showed a lot of poise defensively," Sacco said. "I'm real pleased with that. He made an outstanding play on the 2-on-1 right before he scored the goal when we made a bad decision with the puck. He made a great play to deny the 2-on-1 there."
Mired in a 2-for-22 drought on power plays, the Avalanche tied the game at 6:06 on O'Brien’s first goal of the season with Edmonton's Jeff Petry off for slashing. O'Brien was about 45 feet out when he launched a shot that sailed over Dubnyk's glove.
"To be honest with you, I didn't get everything on it, but it had eyes," O'Brien said. "It's hard enough to score goals, so any time it goes in, obviously I was pretty excited. We needed a win tonight no matter how we did it. It's only one win, but it's much easier now to get a little more confidence going."
The Oilers grabbed a 2-1 lead on a goal by Ryan Jones at 2:24 of the second period during a three-on-two rush. Avalanche goalie Semyon Varlamov stopped the original shot by Eric Belanger, but Jones put in the rebound.
The teams exchanged first-period goals, with Ladislav Smid scoring for the Oilers at 2:59 before Jay McClement responded for the Oilers at 4:35.
Smid, with his first goal in 125 games, was in the left circle when he fired the puck into a half-open net off a pass from Sam Gagner. The play started when Ryan Jones intercepted O'Brien's pass up the middle and fed Gagner breaking into the Avalanche zone. Gagner was stopped by a sliding Varlamov, but he regained possession behind the net and passed to Smid.
McClement knocked a rebound past Dubnyk after Chuck Kobasew was stopped on a two-on-one rush off a pass from Matt Duchene. Colten Teubert was the lone Oilers defender back because partner Theo Peckham was up ice trying to put a hit on Avalanche defenseman Ryan Wilson, who moments earlier hammered Hall in the corner.
Hall's left arm was limp as he left the ice and he managed to return about five minutes later. But Hall left for good late in the period with his shoulder injury after getting cross-checked by defenseman Kyle Quincey, who was assessed a penalty.
"I'm just finishing my checks out there," Wilson said of his hit against Hall. "He put himself in kind of a bad situation, turned back up the ice. It's just one of those things."
1 - 0 EDM
1 - 1 Tie
2 - 1 EDM
2 - 2 Tie
3 - 2 COL