"When we work hard, we know our speed and skill are going to make a difference," Matthews said. "We can't let up on the effort."
Matthews scored twice on the power play for the Maple Leafs, who were 2-for-4 with the man-advantage. They have scored seven times in 14 opportunities this season. John Tavares had an NHL career-high four assists.
[WATCH: All Maple Leafs vs. Red Wings highlights]
"We have a lot of guys who can finish, on this team, especially when we are on the power play," Tavares said. "When I get the puck, I'm just trying to get it to an open player. If that's [Matthews], it is an automatic goal right now."
Mitchell Marner and Morgan Rielly each had a goal and an assist for Toronto (4-1-0). Frederik Andersen made 26 saves.
Matthews, who leads the NHL with nine goals, became the third Toronto player to score in the first five games of a season, joining Sweeney Schriner of the 1944-45 Maple Leafs (nine goals in six games), and Corb Denneny of the 1921-22 St. Patricks (seven goals in five games).
Video: TOR@DET: Matthews wrists one past Howard for PPG
"He had a fast start last year, too, but unfortunately he got injured," Maple Leafs coach Mike Babcock said. "He's a big man, and he's worked hard on every part of his game. He's a better player this year both with the puck and without the puck."
Rielly has 12 points (three goals, nine assists) in the first five games -- the most by an NHL defenseman in his team's first five games in 100 years. Bobby Orr had 11 points (two goals, nine assists) for the Boston Bruins in 1973-74. Harry Cameron scored 15 points (nine goals, six assists) for the Toronto Arenas in 1917-18.
Rielly didn't want to talk about his own numbers.
"I'm not going to address my personal achievements," he said. "I think it is more important to move on."
Video: TOR@DET: Rielly finishes off Marner's sweet feed
The Red Wings (0-2-2) hadn't lost the first four games of a season since going 0-5-0 in 1980-81.
"I think we learned we need to compete for 60 minutes if we want to win games," Red Wings coach Jeff Blashill said. "When we play hard we can make some good things happen, but we have to do that for 60 minutes."
Nick Jensen, who hadn't scored in 87 games, had two goals for Detroit, and Jimmy Howard made 30 saves.
"It's exciting any time you can contribute offensively to the team," said Jensen, who had his first multigoal NHL game. "It isn't as sweet when you get the goals and don't get the win, though."
The Red Wings took a 1-0 lead at 7:18 of the first period when Jensen scored to finish a 3-on-1 break.
Rielly tied it 1-1 at 15:48, one-timing a Marner pass inside the far post.
"Morgan is playing great hockey right now," Marner said. "He's running things on the power play and making chances for everyone, but he also knows when to jump into the rush at even strength."
The Maple Leafs scored twice in the second period and outshot the Red Wings 15-5.
Video: TOR@DET: Matthews, Tavares combine for PPG
Marner made it 2-1 at 2:00, and Matthews extended the lead to 3-1 on the power play at 7:30 on a pass from Rielly.
"Their skill players outcompeted our skill players in the second period, and they won every puck battle," Blashill said. "You see how that affected the game."
Jensen cut it to 3-2 at 10:18 of the third, knocking in his own rebound, but Matthews' power-play goal at 11:11 moved Toronto's lead to 4-2.
Dylan Larkin made it 4-3 on the power play at 13:56, but Ron Hainsey scored a 200-foot empty-net goal at 19:39 for a 5-3 Toronto lead. Hainsey shot the puck behind his own net and around the boards, trying to clear the zone, but it hit a stanchion and deflected in for his second goal.
Video: TOR@DET: Hyman, Marner combine for quick strike
They said it
"I didn't like the third period. We didn't take care of the puck, and we didn't keep our foot on the gas." -- Maple Leafs coach Mike Babcock after his team was outshot 18-9 in the third period
"Nick didn't have a good camp so we sat him out of the first game of the season. He came back for the second game and was great, and he's been great ever since. He was excellent tonight." -- Red Wings coach Jeff Blashill on Nick Jensen
Video: TOR@DET: Jensen buries own rebound for second goal
Need to know
Matthews matched Alex Ovechkin, who scored nine goals in the first five games for the Washington Capitals last season. That hasn't happened since the 1920-21 season. … Tavares has 11 three-assist games, most recently for the Islanders on March 18 against the Carolina Hurricanes. … Red Wings forward Christoffer Ehn got his first NHL point with an assist on Jensen's first goal.
Maple Leafs: At the Washington Capitals on Saturday (7 p.m. ET; NHLN, CBC, NBCSWA, NHL.TV)
Red Wings: At the Boston Bruins on Saturday (3 p.m. ET; NESN, FS-D, NHL.TV)
Video: Matthews nets two, Tavares adds four assists in win