La Cañada had enough chances to pull away from the Vikings, but their goalie, Jack Schwartzman, came up big with 12 saves.
Allen Morovati led the way offensively for the Spartans, scoring a game-high four goals, including two in the first and fourth quarters.
"We've been working a lot on getting him the ball down low in practice," said the Spartans' Chase Borisoff, who had a goal and two steals in the match. "He played great today, he just dominated."
La Cañada took a 4-2 lead at the end of the first quarter, as Morovati scored the Spartans' first two goals, with 4:19 and 3:06 left in the first quarter, for a 2-1 lead after Santa Monica's Jackson Hauty matched his first goal on a man-advantage.
The Vikings' Charlie Olsen answered right back on another six-on-five opportunity to tie the game at 2 with 2:20 left. The Spartans defense forced 16 turnovers and turned six of them into goals Wednesday, but Santa Monica scored five of its six goals on man-advantages.
"I thought our defense, at full strength, was very good," Neville said. "We just had some questionable ejections called on us."
The Spartans went on a two-goal run to close out the first, as Alden Geller and Ryan Gokey scored in the final 1:11 of the opening quarter. La Cañada kept the momentum going on a 3-1 run in the second quarter behind two goals from Trevor Roszkos and another from Symeon Stefan with 25 seconds left in the half, giving the Spartans a 7-3 lead headed into halftime.
Santa Monica was able to trade blows from there, but couldn't put together a run of its own, as both teams scored three times in the third quarter. Hauty finished the game with three goals, matching goals from the Spartans' Chase Borisoff and Stefan in the third, as the Vikings went into the fourth down, 10-6.
Borisoff knows his team will have to be able to do more than trade punches in the next round, though.
"We definitely could have played a lot better," Borisoff said. "It was an overall good effort, we're just going to have to work on some stuff in practice."
The Spartans were able to hold Santa Monica to just one goal in the final quarter, while Morovati scored his final two more goals to seal the 12-7 win.
"We are going to have to play a lot better," Morovati said. "If we play like that in the next round it's going to be a lot closer."
Stefan had three goals in the match, while Geller and Roszkos had two each for La Cañada. Wolfie Paulson had nine saves in goal for the Spartans, who will face Aliso Niguel at Pasadena City College Saturday in the second round of the playoffs.
"We expected this [win]," Neville said. "We'll be playing at home [Saturday] and we'll be ready to go."