Suarez, a gold medallist in the 2001 Southeast Asian Games, totaled 4384 pins after 20 games for a 219 average as he trailed Bill Hoffman of the United States by 275 pins going into the next stage of the qualifiers another 12-game series among the top 24.
Hoffman, 29, topped the first part of the elims with 4659 for a 232.95 average and an 84-pin lead over Belgiums Chris Van Damme and a 210-pin margin over 1988 mens champion, Mohammed Al-Qubaisi of the UAE after 20 games.
Defending champion Mika Luoto of Finland is in seventh place with 4,342 pins and a 217.7 average.
Canare, on the other hand, rallied to finish with 4169 (208) and jump from 11th to No. 7 although she stood 414 pins behind elims topnotcher Marie Ramirez of Costa Rica who rolled a 20-game series of 4583 for an impressive 229 average.
Fancied Shalin Zulkifli of Malaysia placed second with 4421 pins and a 221 average, while defending champion Shannon Pluhowsky of the US is in third with 4394 and a 219 average.
The top 24 men and women thus advanced to the next round of the competitions beginning Thursday morning. Following 12 more games of qualifying, both fields will be cut to the top eight for the quarterfinal round of Friday.
Honduras Gil Valle Suarez and Maria Elena Breve Ferrari failed to advance. Suarez finished 60th with 3724 pins and a 186.2 average. Ferrari wound up in 32nd place with 3720 pins and a 186.0 average.