After a 10-match winless league run, Omiya's hopes of avoiding the drop appeared slim but, under new boss Hiroki Shibuya, they won back-to-back top-flight matches to reinvigorate their survival fight.
However, Frontale, who are second in the table, headed to the NACK5 Stadium eager to put Saturday's 0-0 stalemate with Tokyo behind them and they did just that with a convincing 3-1 win.
Okubo proved the difference, opening the scoring in the 21st minute before doubling his tally five minutes after the break.
The 32-year-old then took his J-League goal total for the season to 15 by putting the game beyond doubt with 11 minutes left on the clock, before an own goal from Yusuke Tanaka in the close stages handed Omiya a consolation.
Frontale remain six points off top spot, though, as leaders Urawa Reds were 2-0 victors at mid-table Albirex Niigata, goals in each half from Shinzo Koroki and Ryota Moriwaki proving enough for three points.
The race for the third and final AFC Champions League spot continues to excite in the J-League and Kashima Antlers moved into third thanks to a 1-0 triumph at Vegalta Sendai, Shoma Doi's strike enough to consign the hosts to a fifth straight defeat - leaving them just two points above the drop zone.
Sagan Tosu had started Tuesday's play in third, but they fell to a 2-0 setback at Kashiwa Reysol thanks to two goals in the space of eight second-half minutes from Masato Kudo.
Gamba Osaka remain in the hunt for a position in continental competition as Kenta Hasegawa's men ran out comfortable 3-0 winners at Shimizu S-Pulse, who remain mired in relegation trouble.
Elsewhere, Tokyo routed rock-bottom Tokushima Vortis 4-0 at the Ajinomoto Stadium and Ventforet Kofu secured a precious three points in a 2-0 triumph over Vissel Kobe.
In other matches, Cerezo Osaka failed to escape the drop zone after losing 2-1 at home to Nagoya Grampus and Yokohama F Marinos defeated Sanfrecce Hiroshima 1-0.
