The Flames chose centre Sean Monahan of the Ottawa 67s sixth overall with their first of three picks on Sunday, and then went for two other forwards with later selections.
Monahan had 78 points this year in the Ontario Hockey League.
"I'm going to do whatever I can to make that team better," said Monahan, to TSN, after his pick in the six slot.
He's also ready to compete for a spot in the lineup this fall.
"I believe so," he said. "I'm working hard this summer, and that's my goal."
Calgary used the second of its picks, 22nd overall, on winger Emile Poirier, of Gatineau in the Quebec league. A fast skater, Poirier had 32 goals and 70 points to go with 101 penalty minutes this year.
Finally, at 28, the Flames went for a hometown youngster, choosing Morgan Klimchuk of the Regina Pats. A left winger, he had 36 goals and 76 total points in 2012-2013.
Edmonton Oilers chose defenceman Darnell Nurse, of the Sault Ste. Marie Greyhounds, with the seventh pick of the day.
Nurse, the son of former CFL receiver Richard Nurse and nephew of former NFL star Donovan McNabb, had 41 points and 116 penalty minutes this past campaign. He was also the OHL's Scholastic Player of the Year,
Then the Vancouver Canucks turned the first round around by trading goaltender Cory Schneider to the New Jersey Devils for the 9th pick, one they used to take centre Bo Horvat, of the London Knights.
Horvat scored 33 times this season, adding 28 assists in 67 games for the top flight OHL team.
He also had 16 goals in the playoffs, and came up with the game-winning goal in Game 7 of the league championship against Barrie with 0.1 seconds to go. That helped earn him the MVP of the Ontario post-season.
Vancouver's second pick of the round, No. 24, was used to take Hunter Shinkaruk, a left winger with the Medicine Hat Tigers. He had been expected to go a but higher.
Senators go with Lazar
Ottawa, one of the most successful teams in the league in recent drafts, had the 17th pick and used it on Curtis Lazar, a winger with the Edmonton Oil Kings who had 38 goals and 61 points this past season.
General manager Bryan Murray said Saturday he believed the Senators could get a "good player" at No. 17. He was listening to offers to move up or down in the first round, but nothing materialized.
Winnipeg surprised many observers by going with defender Josh Morrissey with the 13 pick, a jump of at least a dozen places from where some thought the Prince Albert Raider might go.
A left-handed shot, Morrissey had 15 goals and 32 assists to go along with 91 pentalty minutes.
Toronto went to the Quebec league for its pick at 21, choosing defensive centre Fredereck Gauthier from Rimouski. He had 22 goals and 60 points this season, while being one of the best forecheckers in the QMJHL.
The Montreal Canadiens checked in at 25, and they went large with 6-foot-5, 235 pound winger Mike McCarron, from the U.S. development program. He's slated to head for NCAA college hockey this fall.