The goal came on a slapshot from the blue-line with Reto Berra screened by a group of players in front.
Mike Smith had 29 saves to get the victory.
Calgary trailed 2-0 until halfway through the third period when the Flames finally solved Smith, tying the game with goals less than two minutes apart from Bouma and Knight.
Bouma and Knight were among a handful of Flames forwards in the line-up and getting one last chance to impress coach Bob Hartley and try and win a spot on Calgary's season-opening roster.
Due to a serious knee injury, Bouma was limited to just three AHL games last season. That came after a 2011-12 season in which he played 27 games for Calgary and looked to be a good bet to make the team last year.
Known more as a hard-hitting, energy guy - Bouma has just five goals in 61 games between the AHL/NHL the past two seasons. The unexpected offence of four goals in four pre-season games will only help his case.
Knight, who grew up in Alberta, was drafted by the Florida Panthers in the fifth round of 2009. When it became clear this spring he wasn't going to sign with Florida once he finished his fourth year at the University of North Dakota, they traded him to Calgary.
Making Knight an attractive option is he's a natural centre, which is a position of need for the Flames.
After a lifeless opening 20 minutes in which the teams combined for 11 shots, the game's first goal came 1:36 into the second when Doan deflected a point shot by Ekman-Larsson through the pads of Berra.
Berra was making his home debut for the Flames. Acquired last year from St. Louis in the package Calgary got in exchange for Jay Bouwmeester, the 26-year-old has played his entire career in Switzerland.
Later in the period, Ekman-Larsson made it 2-0 on a pretty goal set up by Mike Ribeiro.
Notes: Notable scratches for Phoenix included former Flames David Moss and Derek Morris along with Rostislav Klesla... Not dressed for Calgary were Jiri Hudler (lower body) and Mike Cammalleri (hand), who are both nursing minor injuries. Brian McGrattan also did not play. Hudler and Cammalleri are expected to be ready for the start of the regular season.