Wendy Turnbull and Beth Norton reached the quarterfinals of the $100,000 Virginia Slims of Washington tennis tournament yesterday, the first time either has gotten that far in a Slims event. One of them is destined to go at least a round farther.

Turnbull, 24, upset fourth-seeded Betty Stove, 6-0, 6-2, and Norton blew a big lead, then came back to finish off eighth-seeded Greer Stevens, 6-1, 4-6, 6-2, in the only singles matches of a snowy afternoon session at George Washington University's Smith Center.

The two will meet today at 1 p.m., and the winner will earn at least $5,000 and a berth in the semifinals when the tournament shifts to Capital Centre Saturday. The final is scheduled Sunday noon.

Turnbull, who has finally recovered from the 33-hour flight from Australia when she arrived Saturday, overslept Tennis Association (WTA) that she was supposed to attend. Stove couldn't skip it because she is the WTA president.

When they got on court at 1 p.m., the roles were reversed. Turnbull was in charge all the way, while Stove, who had been playing consistently well since September, seemed to be hibernating. After serving superbly in the crucial stages of her first-round victory over Renata Tomanova Tuesday, Stove gave one of her most miserable performances.

"The meeting was much better than the match," the way, 31-year-old Netherlander said.

Stove, a 6-foot, 155-pounder whose game is powerful but erratic, lost her serve from 40-15 in the second game and never came close to holding it again in the set. She was hitting wildly and having trouble seeing the ball, blowing easy volleys and overheads.

Meanwhile, Turnbull, who rated this victory on a par with ones over Rosemary Casals last September and Francoise Durr in December as her "best wins ever," played to a high standard throughout, returning service well off both wings.

Turnbull has climbed from No. 70 to No. 30 in the WTA computer rankings in the last 12 months. This is the first Slims tournament she has entered without having to qualify, and she skipped the Australian Open to come here. Now she is happy she did.

Norton, 19, is one of the most promising young American players. She was U.S. Junior champ in 1975 when she leapt from No. 30 to No. 1 in the rankings.

Last year she qualified for the first Slims tournament but pulled a hamstring muscle in her opening match and missed the rest of the circuit.

Now, after working intensively with her 22-year-old brother, Tim, a tennis coach in Connecticut, she feels ready to survive and prosper on the women's pro tour.