The Cats led 55-7 in the third quarter but there was no give-up for Rogers which came back in the fourth quarter to score four touchdowns to the Bobcats' three.
Refugio will face another Eagles team - the Lexington Eagles in the regional quarter final at a time and place not yet determined.
Woodsboro 36, Bruni 21 - FINAL
Mason 35, Three Rivers 13 - FINAL
Blanco 21, Karnes City 14 - FINAL
Lago Vista 35, George West 28 - FINAL
Falls City 33, Sabinal 0 - FINAL
D'Hanis 35, Runge 28 - FINAL
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