The Spartans finished with a 14-6-5 record this season and looked to Bagramyan for most of their offense, as the junior had a hand in 38 of La Cañada's 55 goals this season, as he scored 23 times and notched 15 assists.
St. Francis' Matt Laterza earned a spot on the Division I first team. It was his first All-CIF honor.
La Cañada's Aidan Tourani and Jeff Becker also picked up their first All-CIF awards, being named to the second and third teams, respectively.
Laterza, a senior midfielder/forward, finished with a team-high 13 goals and six assists after being shifted to forward and helped the Golden Knights advance to the second round of the playoffs.
Laterza said things fell into place for him after making the seamless position transition.
"I worked hard and wanted to do anything I could to help our team," Laterza said. "My teammates were the ones who helped me out.
"To get this honor is great."
Said St. Francis Coach Glen Appels, whose team took third in the Mission League: "He's a fun player to coach and a good teammate to have. He deserves the recognition."
Tourani emerged as the Spartans' best defender this year as a junior.
"I know a lot of coaches notice him," Harrison said. "He wins a lot of balls in the air and is real aggressive, real physical. It's hard not to take notice of something like that."
Becker finished his senior season with eight goals and 13 assists, both second best behind Bagramyan.
"It's a great cap to his career to be named All-CIF team," Harrison said. "It's a nice way to send out a kid who was a leader on his high school team the past few years."
St. Francis' Thomas Banks was named to the third team after registering one goal and two assists. The senior defender served as one of the Golden Knights' top defenders.
-Charles Rich contributed to this story.