Andrew Ference's slapshot from the blue-line missed the net but caromed off the boards and out the other side where Boyd banged it in from a sharp angle.
Boyd was one of two forwards called up from Omaha of the American Hockey League on Friday to take the places of Jarome Iginla (knee) and Chuck Kobasew (concussion), who were both hurt in Thursday night's win over the Florida Panthers.
It was the sixth game for Boyd, who had two assists in five games earlier in the season.
Alex Tanguay completed the scoring into an empty net with 27 seconds remaining.
Byron Ritchie added a pair for Calgary (21-15-4), while Tanguay added two assists for a three-point night.
Winners of four of their last five, the Flames move into sole position of second spot in the Northwest Division, one point back of Vancouver.
Daryl Sydor and Jere Lehtinen scored for Dallas (26-16-1). Rookie forward Loui Eriksson had two assists for his first career multi-point game.
Like the Flames, the Stars iced a depleted line-up without defenceman Sergei Zubov - the latest to land on the sidelines, missing his first game of the season due to back spasms. The Stars were already persevering without captain Brenden Morrow (ankle), Mike Modano (hip), and Eric Lindros (ribs).
The absence of the Flames top two right-wingers in Kobasew and Iginla led to some line shuffling by coach Jim Playfair, and Ritchie was one of the benefactors moving up to the second line alongside Matthew Lombardi and Tanguay.
The new trio wasted little time establishing chemistry with Lombardi and Tanguay combining to set up both of Ritchie's goals.
Tied 1-1 after the first period, Ritchie's second of the night gave Calgary its first lead of the night 1:17 into the second.
Similar to the first goal, Tanguay spotted an open Ritchie in front of the net, where Ritchie beat Marty Turco inside the post on a one-timer.
Ritchie's first career two-goal game gives him six goals on the season, surpassing his previous high of five, which he accomplished while with the Florida Panthers.
Dallas answered back at 11:15 of the second period, tying it on their second power-play goal of the night on as many opportunities. Eriksson and Jeff Halpern combined to neatly set up Lehtinen circling out from behind the net, tucking a shot behind Miikka Kiprusoff, who was trapped out of position.
Things didn't look good early as Dallas chalked up the first nine shots on goal before the Flames other call-up from yesterday - Carsen Germyn - registered the Flames first shot at the 10 minute mark.
However, despite being outshot 11-6 in the opening 20 minutes, Calgary was tied 1-1 thanks to Ritchie's goal at 16:53.
Dallas opened the scoring at 9:09 when Sydor got the puck at the side of the net and put a high shot past Kiprusoff from a sharp angle. It was Sydor's first goal in 34 games.
Kiprusoff was the busier of the two goalies finishing with 31 saves compared to 17 for Turco.
Notes: - Calgary RW Tony Amonte was elevated onto the Flames top line alongside C Daymond Langkow and LW Kristian Huselius... The last game Iginla missed was Jan. 19, 2004. The one game he missed at that time with a sore knee is the only previous time Iginla has missed NHL action with any type of leg injury. Since then, Iginla had appeared in 158 straight games ... The 11 games Iginla missed with a hand injury in 1997-98 (Jan. 24 - Mar. 5, 1998) is the longest stretch of games he has missed in his career... Calgary is unbeaten (4-0-2 ) in the last six games Iginla has missed. In the 31 games Iginla has missed in his career, the team is 15-11-5.