Lee initially led, 1-0, before Law won back-to-back tight games in pulling ahead, 2-1.
That's when Lee countered with four straight game victories in taking a 6-2 advantage en route to a five-game victory in the eight-point, one-set style match.
"As long as I focused and concentrated on each point, I thought I would be able to come back," Lee said. "There have been times before that I hadn't done that."
Lee advanced to the quarterfinals by outlasting South Pasadena's Eren Cameron in the first round, 9-7.
The only other Spartans competitors to advance past the first round was the doubles team of juniors Leeho Lim and Harrison Zuk.
The pair defeated South Pasadena's Kyeong Min and Krishna Mocheria, 8-2, in the first round before falling to second-seeded Robert Carter and Daniel Gealer of San Marino, 8-3.
Despite the odds, Lim and Zuk challenged the Titans' top twosome, taking them to game-point on four separate occasions, while trailing 4-1, 5-2 and 6-3.
"We were down love-four and we lost three of those four games on deuces," Lim said, referring to the no-advantage scoring system used. "We play no-ad scoring in this league and it's not a good system. In CIF, it's not that way, but that's the way it is in league."
When informed his doubles team was one of only two Spartans entrants that survived to the quarterfinals, Zuk wasn't that enthused.
"I guess that's a good thing," Zuk said.
In other action, La Cañada's Joe Song and Liwon Lim were defeated in doubles first-round action, 8-6, by South Pasadena's Scott Richards and Phillip Kim, while the doubles team of Christopher Madsen and Patrick Finnigan defaulted.
As for singles play, Law bounced La Cañada's David Oh in the first round, 8-6, while the Spartans' Arthur Song was topped by San Marino's Matthew Hsiao, 8-1, also in the first round.
"We had some tough draws and we had a lot of guys missing this week," La Cañada Coach Will Moravec said. "Our No. 1 player, Joshua Kim, had an asthma attack a couple of weeks ago and has been out since ... and we were also missing two seniors who were preparing for AP testing.
"So, overall, I was pleased with what we accomplished and that we'll have at least one player at finals."
While Wednesday's play was decided in one set, Thursday's semifinals will require a standard two-out-of-three set victory.