Abadia, who will make his SEA Games debut in Vietnam next month, is now 7-3 over Lazaro, including a semifinal victory in this years AFP Olympics.
"Medyo nagkumpiyansa ako sa second set kaya nakuha ni Lazaro. Yung forehand niya, kung nakakapuwesto, mahirap ibalik," said Abadia, who played several times for the RP Davis Cup team.
"Nag-iba din yung laro ni Lazaro. Dati, hindi naman siya pumapasok sa net, pero ginawa niya ngayon," added Abadia, who will next play top seed Korean Hee Seok-Chung.
Chung, ranked No. 703 in the world, scored a 6-4, 6-0 victory over No. 14 and Escudero Cup champion Chemiel Mantua.
Other winners were second seed Johnny Arcilla over Joel Palao, 6-3, 6-3, fourth seed and defending champion Joseph Victorino over No. 13 Jesse Lapore, 6-1, 6-2, fifth seed Adelo Abadia over No. 9 Alexander Lazaro, 6-1, 6-7 (4), 6-3, and sixth seed Rolando Ruel Jr. over No. 11 Michael Mora III, 7-5, 7-5.
Earlier, top seed Anna Patricia Santos, second pick Alyssa Anne Labay, and fourth seed Czarina Mae Arevalo downed separate rivals to gain quarterfinal slots.
Santos, whose title victories in the Olivarez Cup, Coca-Cola Open and the Hilado Open this year gave her the No. 1 ranking, scored a 6-4, 6-1 win over No. 13 Aileen Rogan to advance against the winner between No. 7 Ivy de Castro and No. 11 and national soft tennis player Divine Escala.
The second-ranked Labay of Bacolod City downed Annie dela Peña, 6-2, 6-4, to advance against sixth seed Deena Rose Cruz, a 6-4, 6-4 winner over La Salles Bernardine Sepulveda.
Arevalo, the defending champion and fourth seed, blasted Hazel Tanedo, 6-0, 6-0, to advance against fifth seed Michelle Panis, who posted a 6-2, 6-2 victory over unranked Julie Em Botor.
Lucena City-based Bien Zoleta, the third seed who won last months Escudero Cup, rallied past Karen Reyes, 1-6, 6-2, 7-5, to forge a quarterfinal showdown with No. 8 Josephine Paguyo, who beat No. 10 Catherine Flores, 7-5, 6-4.
Meanwhile, defending mens doubles champion Johnny Arcilla and Michael Mora III demolished Gabby Remigio and Karl Santamaria, 6-2, 6-0, to reach the third round of this event presented by Dunlop and sponsored by Diadora, PLDT, Procter and Gamble, Coca-Cola, Copacabana, San Miguel Corporation, Stronghold, Little Lawrence, PVL Restaurant and the Star.
Also advancing were No. 4 Koreans Seung Hoon Lee and Eui Hyun Chung, No. 5 Beeyong Sison and Junjun Toledo, No. 6 Chemiel Mantua and Pop Sabandon, No. 7 Adelo Abadia and Joseph Victorino, No. 8 Jesse Lapore and Jaime Solon, No. 9 Elbert Anasta and Antonio Sagansay III, No. 14 Rocky Paglalunan and Mario Sabas, Terrence Estrope and Rollyto Litang, Derrick and Duane Santos, Julius Kraut and Michael Misa, Adonis Lominoque and Fritzgerald Tabura, Ramil Buenaventura and Jessie Magat.