Reyes, a former world 9-ball champion raring to rule this 8-ball event which offers $350,000 to the winner, trounced American Earl Strickland, 8-5, whipped Raj Hundal, 8-1, outplayed Marko Lohtander, 8-5, then subdued Gary Abood, 8-6, in Group 62 to record one of the five sweeps posted in the day.
Lining followed suit with victories over Mika Immonen (8-6), Sandor Tot (8-6), John Schmidt (8-2) and Jimmy Wetch (8-4) in Group 65 while Manalo defeated Charles Williams (8-2), Gabriel Owen (8-5), Sarah Ellerby (8-0) and compatriot Ronnie Alcano (8-2) to top Group 70.
Francisco "Django" Bustamante, the former world No. 1, won two and lost two to barely make it to the next round where each of the 36 survivors is assured of $17,000.
Fil-Am Santos Sambajon, who had an impressive stint in the second round, struggled this time, dropping two of his first three games before beating Jon Kucharo, 8-5, in the final game to snatch the third and last spot in Group 69.
Other Filipino bets who advanced to the fourth round were Alcano, Dennis Orcollo, Rodolfo Luat and former world 9-ball champion Alex Pagulayan.
But the race to the finals is expected to heat up among the Filipinos in the fourth round with Reyes, Bustamante and Sambajon bunched in Group 74 and Pagulayan, Orcollo and Luat clashing in Group 76.
Alcano, Manalo and Lining are the lone Filipino players in Groups 73, 75 and 77, respectively, all hoping to clinch one of the three berths staked in each group.
Still, focus will be on Group 74 where Reyes, Bustamante and Sambajon fight it out with Michael Hill, Gabriel Owen and Ivica Putnik.