Perron took a centering pass from Larkin in the right slot and beat Korpisalo with a quick shot on the power play to make it 3-1 at 14:54.
"Second period's got to be better," Greig said. "We can't get outworked like that in our building. Hopefully it doesn't happen again."
Larkin made it 4-1 just 28 seconds into the third period with a wrist shot from the slot on the power play.
"We had some big-time breakdowns on the penalty kill," Ottawa coach D.J. Smith said. "We took too many penalties, but you've got to kill them. And we just didn't look good in that department."
The Red Wings extended the lead to 5-1 at 7:23 scoring off a turnover when Veleno took a cross-ice pass from Daniel Sprong on the rush and scored short side on Korpisalo. It was Veleno's first two-goal game in the NHL.
"It was obviously two great players that made two awesome plays for me," Veleno said of his two goals. "I was happy I was able to be in the right spot at the right time."
Greig scored on a wrist shot at 8:49 for the 5-2 final.
"Definitely not the effort we want, ever," Tkachuk said. "I don't think that will happen again."
The Red Wings lost back-to-back games at the Senators last season (6-2 on Feb. 27; 6-1 on Feb. 28), which began a 7-15-2 stretch to end the season.
"We all remember what happened when we came in here last year," Veleno said. "We didn't want to let that happen again. I think we came prepared. We knew what we were facing. They're a [heck] of a team down there and I think they will be for a while. We came to play today."
NOTES: Larkin has nine points (two goals, seven assists) during a five-game point streak, and Gostisbehere has six points (two goals, four assists) during a five-game point streak. … Detroit had lost its past five games at Ottawa, dating to Oct. 23, 2019. … The Red Wings have their most wins through the first five games of a season since 2017-18 (also 4-1-0). … Detroit has scored 24 goals, the third-most in its first five games of a season (25 in 1942-43 and 1972-73). … Senators forward Tim Stutzle did not have a point for the first time in five games this season.