Rieder scored two short-handed goals in 58 seconds on the same penalty kill, and the Arizona Coyotes beat Edmonton 5-2 to hand the Oilers their 10th consecutive loss.
''I obviously wasn't expecting anything like that,'' Rieder said. ''It is just amazing that we scored two short-handed goals. That was really exciting. I'm not sure if I really realize what happened yet. It's pretty hard to even score goals on the power play in this league, let alone to get two short-handed that quickly.''
Oliver Ekman-Larsson, Mikkel Boedker and Martin Erat also scored for the Coyotes, who snapped a three-game skid and won for the second time in seven games. They extended their point streak against Edmonton to a franchise-record 16 games.
''Now is an important time for us,'' said Coyotes goalie Mike Smith, who snapped his seven-game losing streak. ''It is a lighter month for us and we need to get back in the hunt before Christmas. We are done talking and having meetings. We know what we have to do now. It's just about going out there and doing it.''
Jordan Eberle and Jeff Petry each had a goal for the Oilers (6-15-4), who have not won at home since October. They dropped to 0-12-3 against Western Conference opponents.
Edmonton captain Andrew Ference said there's simply no excuse for starting the second period on the power play with a 1-0 lead and allowing two short-handed goals.
''Guys are letting their guard down, and we're in no position to be doing that - to be taking a rest and relaxing. We start the period with a power play and we're looking for some jump. You're looking for some momentum and it's a matter of falling into old habits, floating around and expecting the other team to lie down because you're so great,'' Ference said. ''It doesn't happen, we made the same mistakes, it cost us games and it definitely puts you in a hole again. We allow two on the same power play, it's a joke.''
Ference said something clearly has to change for the Oilers.
''The definition of insanity is doing the same thing over and over again when it doesn't work,'' he said. ''Do you try it again or look for a different path? I think that you've seen that with some of the mistakes, that's what it is, insanity.''
Leading by a goal, Edmonton came unraveled early in the second.
Just 36 seconds in, Taylor Hall coughed up the puck in the neutral zone and Rieder went in on a breakaway, tucking his third of the season through Viktor Fasth's legs.
Rieder scored again on the same Edmonton man advantage at 1:34 after Martin Hanzal blocked a shot and sent the former Oilers draft pick up the ice with speed. Rieder outraced defender Nikita Nikitin before cutting in on net and scoring.
''I wish I could have made at least one of those two saves and kept us in the game. But they scored four in the second period and we didn't manage to battle back,'' Fasth said.
The Coyotes made it 3-1 with their third goal in a span of 4:17 when Ekman-Larsson scored a power-play goal on a shot through traffic from the slot.
Edmonton started to push back a little just past the midway point of the second period, but Smith came up with huge saves on Mark Arcobello and Tyler Pitlick to maintain the two-goal advantage.
Arizona went up 4-1 with 17 seconds left as Boedker picked up a loose puck in front and showed deft hands to corral it and tuck in his eighth of the season.
''I'm glad that the leadership in this room came out and grabbed this game,'' Coyotes coach Dave Tippett said. ''We played a lot of the game the right way. Our special teams were excellent, obviously with Toby getting those two short-handed goals, but also getting a couple on our power play. It was a much-needed win.
''Now the challenge is to continue this night in and night out.''
The Coyotes took a four-goal lead at 2:03 of the third on the power play. Michael Stone's shot went wide but came off the boards right to Erat at the other side of the net.
A couple of minutes later, Petry's point shot deflected off a Coyotes defender in front and past Smith to make it 5-2.
NOTES: The Coyotes are right back at it Tuesday when they visit Calgary. The Oilers make a one-game trip to Winnipeg on Wednesday. ... Arizona has won the first three meetings between the teams this season. They play five times. ... The Coyotes last lost in regulation to Edmonton on Jan. 25, 2011. ... Tippett is 18-2-3 against Edmonton during his Coyotes tenure. ... The longest winless streak in Oilers history is 14 games, from Oct. 11 to Nov. 7, 1993. ... Pitlick made his season debut after being recalled from the Oklahoma City Barons of the AHL on Sunday. ... Out with injuries for the Oilers were Benoit Pouliot (foot) and Matt Hendricks (leg). The Coyotes were without David Moss (hand) and Brandon Gormley (lower body).