Chelios, the NHL's oldest player at 45, skated in his 1,550th game, breaking a tie with Hall of Famer Alex Delvecchio to move into eighth place on the career list.
The Red Wings, who had 35 shots, dominated the play most of the game, but allowed both goals on rushes in which two Detroit skaters went to the same area of the ice in their own end and left the eventual goal scorer wide open.
"Defensively, we have to do a better job of sorting out our own end," said Lidstrom, the team's captain.
"Against a team like that, that's a puck control team, they're going to possess the puck," said Horcoff. "That's okay with us as long as we keep them to the outside. When we got in trouble was when we let them inside."
Cogliano's goal, with 10 seconds left in the second period, cut the Red Wings' lead to 3-2.
"We were in pretty good shape after two periods," said Oilers' coach Craig MacTavish.
But Detroit held off the Oilers in the third period and Draper added an empty-net goal with 33 seconds left.
The Red Wings blew a third period lead in Saturday night's 4-3 shootout loss at Chicago, so they were especially determined to not let it happen again on Monday night.
"We didn't give them the neutral zone, didn't give them too many chances," said Hasek.
Holmstrom gave Detroit a 3-1 lead with a power-play goal 27 seconds into the second period. He shoved in a loose puck from a goal-mouth scramble for his third goal in three games.
Zetterberg is also off to a fast start with seven points on a goal and six assists.,
"It's always nice to get some points on the board," he said. I've had some easy assists."
Detroit led 2-1 after the first period.
Samuelsson opened the scoring at 6:51 on a wraparound play. It wasn't officially a power-play goal, but came exactly two minutes after Edmonton defenseman Steve Staios went off for tripping Dan Cleary. So the chance was generated with the man advantage.
"We took too many penalties early," said MacTavish.
Chelios made it 2-0 when he put in his own rebound on his third shot of the sequence with 5:50 left in the opening period. It was Chelios' first regular-season goal in 77 games, dating to April 8, 2006.
Horcoff made it 2-1 just 19 seconds later when he beat Hasek with a wrist shot from the slot.
Detroit F Johan Franzen missed his first game after spraining his knee Saturday night against Chicago. He's expected to miss three to four weeks. ... Edmonton LW and captain Ethan Moreau has yet to play this season because of a left ankle contusion from the preseason. ... Lidstrom's two assists gave him 873 points, breaking a tie with Peter Forsberg, for the second-highest total among Swedish-born players in history. Toronto's Mats Sundin is first with 1,249.
Copyright by STATS LLC and The Associated Press
Arena: Joe Louis Arena Location: Detroit, Michigan
Referees: Michael McGeough, Mike Hasenfratz Linesmen: Pierre Racicot, Derek Amell
Attendance: 16,913 (84.3% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Mikael Samuelsson (1)
Assists: Daniel Cleary, Nicklas Lidstrom
Chris Chelios (1)
Assists: Mikael Samuelsson, Jiri Hudler
Shawn Horcoff (1)
Assists: Ales Hemsky, Dustin Penner
Tomas Holmstrom (3)
(Power Play) Assists: Henrik Zetterberg, Nicklas Lidstrom
Andrew Cogliano (1)
Assists: Joni Pitkanen, Robert Nilsson
Kris Draper (1)
(Empty Net) Assists: Pavel Datsyuk, Henrik Zetterberg