Kari Lehtonen made 17 saves for the Stars, who had been outscored 21-4 during the five-game skid.
Before the game, Gaglardi was introduced to the crowd and dropped the puck for the ceremonial faceoff. The Canadian businessman's purchase of the team was approved by the NHL last week.
"You spend a quarter of a billion dollars, it would be nice for you to get a win," Stars coach Glen Gulutzan said.
"The guys were playing for themselves, obviously, but we talked with Tom this morning and he had a good message for our guys and you could tell in the pregame skate that our guys were a little lighter on their feet and had a little more confidence. It's nice to get one for him when he's in the house. It's a nice way to start to own a franchise."
Radek Dvorak wrapped up the win with a short-handed empty-netter with 1:24 left, Dvorak's first goal of the season.
Rookie Ryan Nugent-Hopkins, who had five assists in the Oilers' 9-2 win over Chicago on Saturday night, scored his eighth goal of the season for Edmonton.
The Stars grabbed early momentum with a physical approach and aggressive forecheck that kept the Oilers bottled up in their own zone. Dallas built a 14-7 shots edge in the first period.
"We didn't handle it very well," Oilers coach Tom Renney said. "We have assets that can intimidate, too. They had us on our heels and we didn't respond real well the first part of the game. We didn't measure up when we needed to."
Petersen got his first of the season from low in the left circle at 8:30 of the opening period.
Edmonton had a chance to tie with about five minutes left in the first period, but Ales Hemsky's shot rang off the crossbar.
Ott made it 2-0 off Mike Ribeiro's setup at 8:58 of the second period, Ott's third of the season. Brenden Morrow also assisted for his 500th career point.
Nugent-Hopkins connected from the slot to get Edmonton on the board at 15:24 of the second, but Ryder fired into the upper right corner of the net off a 4-on-1 break 50 seconds later for his seventh of the season to give Dallas a 3-1 advantage.
Dallas' penalty killers had a good night, denying Edmonton on all six power plays.
Overall, Gaglardi had to be pleased with what he saw, although home attendance continues to lag for the Stars. Monday night's crowd was announced as 11,458.
Still, the Stars earned their first home victory since Nov. 4.
"Hopefully now that will get our confidence back up and remove some of the doubt that creeps into your minds during those kinds of slides," Petersen said.
"Those slides are going to happen every season, but hopefully we got it out of the way early and that will be it and we'll just move forward and get back on the right track."
D Alex Goligoski (broken thumb) and forward Adam Burish (hand) are both out for at least a month for the Stars. ... Edmonton opened a four-game trip. ... NHL commissioner Gary Bettman participated in Gaglardi's introductory news conference earlier Monday and was at the game. ... The Oilers are without C Sam Gagner (back), D Andy Sutton (groin), D Ryan Whitney (knee) and D Cam Barker (ankle). ... Morrow was whistled for three minor penalties.
Copyright by STATS LLC and The Associated Press
Arena: American Airlines Center Location: Dallas, Texas
Referees: Brad Watson, Marcus Vinnerborg Linesmen: Jean Morin, Mike Cvik
Attendance: 11,458 (61.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Toby Petersen (1)
Assists: Tom Wandell, Eric Nystrom
Steve Ott (3)
Assists: Mike Ribeiro, Brenden Morrow
Ryan Nugent-Hopkins (8)
Assists: Jordan Eberle, Ryan Smyth
Michael Ryder (7)
Assists: Nicklas Grossmann, Loui Eriksson
Radek Dvorak (1)
(Shorthanded) Assist: Vernon Fiddler