The Wales international, yet to get going this term due to a series of niggling injury issues, converted 35 minutes in after Lucas Vazquez was brought down inside the box.
Los Blancos, without a number of star names for this tie in Soria, added a second and third late on in the match once their opponents had been reduced to 10 men.
Following an evenly-contested start to the game at Nuevo Estadio Los Pajaritos, Numancia fashioned the first real shooting chance as Pape Maly Diamanka saw his attempt deflect into the path of Iker Casilla.
A poor clearance from back-up stopper Casilla almost let Higinio Marin in soon after, but his low effort ended narrowly wide of the target.
Madrid finally showed signs of life a quarter of the way through, with Marco Asensio nearly getting a toe on the end of Bale's precise delivery.
Vazquez took the wrong option by blasting into the side-netting, rather than picking out a teammate, and Borja Mayoral shinned a good chance over the bar.
Madrid, far from their best in the first half, looked to build on their advantage through near misses from Asensio and Vazquez either side of the interval.
Higinio was cautioned for a perceived dive in the box, and further punishment was to follow for the Reds as they lost Diamanka soon after to a wild challenge on Nacho.
A smart headed attempt from Higinio aside, Madrid took control from that point on and were able to add some gloss to the scoreline late on following a succession of half-chances.
Substitute Mateo Kovacic, on for Bale with an hour played, led a swift counter that culminated in Vazquez being tripped inside the penalty box.
Isco made no mistake from the spot and Mayoral was able to drift off his marker in added time to round off the scoring with a downward header.
Madrid welcome the Segunda Division promotion chasers to the Spanish capital in six days' time for the return leg.
Numancia (4-2-3-1): Munir; Medina, Calvo, Gutierrez, Ripa (Valcarce 20'); Larrea, Perez (Sierra 63'); Nieto, Diamanka, Milla; Higinio
Real Madrid (4-3-3): Casilla; Carvajal, Vallejo, Nacho, Hernandez; Ceballos (Isco 74'), Llorente, Asensio (Hakimi 85'); Vazquez, Mayoral, Bale (Kovacic 61')