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Primordial black holes (PBHs) provide a well-motivated nonparticle candidate for dark matter, requiring an enhancement of curvature perturbations on small inflationary scales consistent with observational constraints. In this work we study PBH production within Horndeski gravity, accounting for compatibility with the GW170817 constraint on the gravitational-wave (GW) speed and imposing a constant coupling to the Ricci scalar. Under these conditions, and assuming an inflaton field characterized by a canonical kinetic term and a smooth potential, the inflationary dynamics is controlled by the cubic Horndeski interaction. By investigating standard functional forms of the latter we identify the specific kinetic structure that allows enhancement of the effective friction on the inflaton, thereby inducing a transient ultraslow-roll phase embedded within a standard slow-roll evolution. For representative parameter choices we find that pronounced amplifications in the scalar power spectrum are generated, leading to the formation of asteroid-mass PBHs with masses of order <inline-formula><mml:math><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mo>⊙</mml:mo></mml:msub></mml:math></inline-formula>, which can account for a substantial fraction of the dark matter abundance, reaching <inline-formula><mml:math><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>PBH</mml:mi></mml:mrow></mml:msub><mml:mo>≃</mml:mo><mml:mn>0.9</mml:mn></mml:math></inline-formula>, while satisfying current observational constraints. The resulting characteristic features in the scalar power spectrum also imply potentially observable scalar-induced gravitational-wave signatures.