Top-seeded Eddie Dibbs made quick work of his second round singles match against Tom Gullikson last night, posting a 6-4, 6-2 victory at George Washington University's Smith Center.

Playing the final match of the evening, Dibbs used his two-firsted backhand effectively to eliminate Gullikson in 55 minutes after most of the announced crowd of 3,900 had left the arena. The 28-year old Floridian, currently ranked seventh in the world by the Association of Tennis Professionals' computer rankings, will meet Marty Riessen, ranked 54th, in a quarter-final match today at 5 p.m.

The top-four seeds advanced to today's round of eight in singles play. Brian Gottfried, the No. 2 seed, defeated Hank Pfister, 6-4, 6-7, 6-4; No. 3 Arthur Ashe fought off three match points in the third set to turn back Puerto Rican Francisco Gonzalez, 3-6, 6-2, 7-6; and No. 4 Roscoe Tanner eliminated Czechoslovakian Tomaz Smid, 3-6, 6-4, 7-6.

Victor Amaya, the seventh seed, also advanced with a 4-6, 7-6, 7-6 decision over Brian Teacher, but Tim Gullikson (No. 6) and Stan Smith (No. 8) were not so lucky. South African Andrew Pattison easily handled Gullikson, 6-1, -1, while Riessen beat Smith, 6-3, 6-2.

Earlier in the week, No. 5 seed Raul Ramirez was beaten by unseeded Jeff Borowiak, 6-1, 3-6, 6-3. Yesterday, Borowiak defeated Mike Cahill, 6-4, 7-6, 7-3.

The Dibbs-Gullikson match did not start until 11 p.m., largely because it took Ashe 1 hour 50 minutes to slip by the spirited Gonzalez, who appeared to have the tournament's biggest upset in hand.

Gonzalez won the first set handily, 6-3, but Ashe rallied late in the second, breaking Gonzalez's final two serves for a 6-2 victory.