Tied 4-4 with five minutes to play, Eric Tangradi sent a beautiful backhand pass in front to Frolik, who directed his second of the season into the net before Oilers goalie Devan Dubnyk could get back across the crease.
Jacob Trouba also scored and added an assist in his first NHL game for the Jets (1-0-0) who were making their first appearance as a Winnipeg team in Edmonton since 1996.
Edmonton started the scoring just over two minutes into the game as Luke Gazdic took a backhand shot from the faceoff that was later determined to have gone off Brown's stick and eluded Pavelec.
The goal was originally awarded to Gazdic, who was playing his first NHL shift, coming to the Oilers off of the waiver wire from the Dallas Stars on Sunday as Edmonton looked for an enforcer.
The Jets tied the game just over a minute later on the power play as Schiefele picked the corner with a shot from the top of the circle that Dubnyk waved at.
Winnipeg went up 2-1 with just under four minutes to play in the first period as Little took a long pass from Tobias Enstrom at the blue-line before waiting for defender Nick Schultz to go down to block a shot and calmly beating Dubnyk stick-side. It was Little's 100th career NHL goal.
Edmonton tied the game two minutes later on the power play as Gordon tipped in a Justin Schultz point shot for his first as an Oiler.
The Oilers out-shot Winnipeg 15-7 in the first.
Edmonton went up 3-2 three and a half minutes into the second period as Hemsky worked his way into the Jets zone and beat Pavelec with a quick wrist shot from the face-off dot.
The Oilers took a two-goal lead eight minutes into the second with another power-play goal as Jordan Eberle had a couple of cracks in tight before Joensuu pounced on the rebound and put it into the empty net. Centre Mark Arcobello earned an assist for his first NHL point.
The Jets got back into the game with a touch under four minutes remaining in the second period as Frolik was hit by a puck in front but picked it up and swung a shot through traffic past a screened Dubnyk.
Winnipeg tied the game just past the midmark of the third as Trouba intercepted a long Taylor Hall pass attempt and beat Dubnyk with a knuckler from just across the blue-line. It was Trouba's first NHL game.
The Jets are off until Friday when they host the L.A. Kings. The Oilers travel to Vancouver to face the Canucks on Saturday.
Notes: The Jets were making their first regular season visit to Rexall Place since March 1996… Edmonton came into the game with a pretty impressive record of 18-6-3 in season openers at home… The two teams are both hoping to erase long absences from the playoffs. The Oilers have not been in the playoffs since going to Game 7 of the Stanley Cup Finals in 2006. The Winnipeg/Atlanta franchise had not see post-season play since 2007… Trouba, a defenceman and the No. 9 pick in the 2012 Draft made his NHL debut in the game for Winnipeg, earning his first point on an assist on a second period goal. A pair of other defencemen who were question marks with training camp injuries, Dustin Byfuglien and Zach Bogosian were able to play in the season opener in Edmonton… In addition to head coach Dallas Eakins coaching his first regular season game in the big leagues, the Oilers had three players making their NHL debuts in defenceman Anton Belov and forwards Will Acton and Luke Gazdic. Acton had an assist in his first shift on Brown's goal… Oiler forward Jordan Eberle led the league in pre-season scoring with eight points.