The Indians (12-2), who finished as the second-place team in the Pacific League, will take on the winner of the second-round match between Chadwick and Beverly Hills in a quarterfinal contest at 3 p.m. Tuesday at a site to be determined.
Last season, Burroughs advanced to the semifinals for the first time in school history.
"We knew that Burroughs has the best player in the division," Valencia Coach Annie Kellogg said. "I'm just surprised that even though they made it to the semifinals last year, they aren't ranked."
Taking on a Vikings (20-4) team that rolled to a Foothill League championship, the Indians figured that set wins would be at a premium Friday. That was partially because the team was still missing league singles runner-up Calvin Fox, who was out with an injury.
Despite missing a key piece to its lineup, Burroughs was able to take an early lead and make it stand up. The Indians had a 4-2 advantage after the first of three rounds and led, 8-4, after the second round.
"It's high school tennis, it's not life and death," said Burroughs junior Garrett Auproux, the two-time defending league singles champion, who is also a team captain. "We just wanted to go out there and have fun.
"Obviously we all want to win, so we want to go out there, play smart and win every game that we can."
The Burroughs No. 1 doubles team of Kevin Hoang and Phillip Lam — this season's league champs — rolled to 6-4, 6-0, 6-0 results. At No. 2, Wen Yao Lin and Michael Whelan also swept, 6-2, 6-1, 6-4.
The match was clinched when Hoang and Lam defeated Jonathan Ramirez and Sam Rebele, 6-0, in the third round.
As expected, Auproux did his job, winning his three sets, 6-1, 6-0, 6-3. The Indians also received a solid performance from freshman Sawyer Patterson at No. 2, as he went, 6-1, 6-1, 2-6.
"Sawyer getting the two wins was key for us today," Burroughs Coach Roy Bernhardt said. "But the two doubles teams did a very good job, as well."
Burroughs' No. 3 singles and doubles were both swept.