Dayton found Gallegos in open space and delivered a pass to set up the game’s first goal in the 10th minute.
Ruiz scored a few minutes later and then converted a penalty kick in the second half to secure the victory.
No. 1 seed Valley Christian (9-7-4) finished fifth in the tightly packed West Catholic Athletic League and was the last team to beat league champion St. Francis.
Woodside placed fifth in the Peninsula Athletic League Bay Division and had an overall winning percentage of .579 (7-2-0 in non-league play), third best among PAL Bay Division teams.
The Wildcats went 0-3-1 over their last four regular season matches. They opened the season with victories in six of their first eight matches.
Woodside dropped its first round match in last year’s CCS Division I playoffs at home against Watsonville after winning the PAL Ocean Division title.
Menlo-Atherton (7-6-4) also earned a big victory, beating host Menlo School 2-0 in Division II play.
Caden Annison gave the Bears a 1-0 lead in the first half, heading in a crossing pass from from Hewitt Stevenson.
Finn O’Brien also scored on a header. He redirected a corner kick from Shinya Frank in the second half.
Sophomore Chase Trigg made several highlight-reel saves in the net for M-A.
Also in Division II, Sacred Heart Prep beat Sobrato 3-1 and will play Wednesday at Hillsdale, a 3-0 winner over Soquel. Mountain View beat Carlmont on penalty kicks, 4-3. The match was tied 3-3 in regulation.
The Spartans (11-4-5) host Menlo-Atherton on Wednesday.
In the Open Division, St. Francis beat Santa Clara 2-0, scoring both goals in the second half. The third-seeded Lancers (15-5-1) play at No. 2 Watsonville in Tuesday’s semifinal.
In Division I, Wilcox topped Palo Alto 2-0.
In Division IV, Sequoia beat El Camino on penalty kicks 3-1 and will meet Seaside in the semifinals on Wednesday. Sequoia and El Camino were tied 1-1 into the penalty kicks.
Girls soccer
Top-seed Mountain View (19-0-1) beat Burlingame 4-0 in the first round of the CCS Open Division playoffs.
Karena Shah scored twice and recorded an assist for the Spartans, who will host either St. Ignatius or Leigh in Tuesday’s semifinal.
Allie Montoya added a goal and assist and Kate Stone also netted a goal. Charis Toney and Laila Edris each added an assist.
Senior Sophia Sasaki recorded a pair of saves in the net for the Spartans,
Also in the Open Division, No. 2 St. Francis beat Leland 2-1 and will host Mitty in Tuesday’s semifinal.
Mitty knocked off No. 3 Woodside 1-0 in overtime to advance.
Seventh-seeded Menlo School went on the road to No. 2 Live Oak and put on a scoring clinic, returning to Atherton with a 6-0 victory Saturday in CCS Division II play.
Sasha Bernthal scored with an assist from Ellie El-Fishawy less than 90 seconds in and the rout was on.
Sophomore Lila Gold, junior Hannah Gorospe, and freshman Roya Rezaee scored to give Menlo a 4-0 lead.
Freshman Audrey Hochstetler scored off a feed from junior Colby Wilson and Menlo held a 5-0 halftime advantaged.
Bernthal added a late goal as Menlo advanced to the semifinals.
The Knights (11-5-4) will also be on the road for Wednesday’s semifinal round at No. 3 Christopher, a 2-1 winner over Menlo-Atherton (6-7-6).
Christopher (10-5-1) took a 1-0 lead on a corner kick seconds before halftime. The Bears tied it with a penalty kick midway through the second half but Christopher again scored in the final minute to earn the win.
The Christopher goalie saved the match for her team, snatching sure goals away from M-A, once when she came out of the net and blocked a shot with her body at the 15-yard line.
Also in Division II, host Sacred Heart Prep squeezed past Aptos 3-2 and Palo Alto fell in penalty kicks to top seed Piedmont Hills, 4-3. The game was tied 1-1 in regulation. Katherine Thomsen scored for Paly.
Sacred Heart Prep (12-6-3) visits Piedmont Hills (17-2-2) on Wednesday.
In Division I, No. 8 Gunn fell to No. 1 Carlmont, 1-0, No. 6 Sequoia lost at No. 3 Saratoga, 2-1 and Los Altos beat Notre Dame Belmont 7-4.