The Irishman out-sprinted Vuelta leader Primož Roglič (Jumbo-Visma) at the top of the category 1 finishing climb at La Laguna Negra de Vinuesa, the third mountain stage of the first three in the race and Martin's third straight podium finish.
With the time bonus, Martin shaved four seconds off Roglič's lead and now sits five seconds down in second place, with Richard Carapaz (Ineos Grenadiers) in third at 15 seconds.
The 6.5km final climb wasn't enough to create large gaps in the overall contenders, but Movistar tried to force the pace until Marc Soler ran into trouble on the lower slopes and the team were forced to let off the gas to help him limit his losses.
Ineos took over as the climb went on and made life difficult for Esteban Chaves (Mitchelton-Scott) to rejoin after suffering a puncture and swapping bikes with the much taller Tsgabu Grmay.
Nine riders sprinted for the stage win with Martin proving strongest, giving his team their first success in the Vuelta.
Watch the Vuelta a Espana stage 3 highlights above.