The Quick-Step Floors rider timed his run perfectly, capitalising on team mate Michael Morkov's flawless piloting, to finish ahead of Giacomo Nizzolo (Trek-Segafredo) and Peter Sagan (Bora-Hansgrohe).
“It was beautiful," the Italian said, resplendent in his nation's road championship jersey.
"I have no words for the team. It’s difficult to control stages like that, but we really wanted it.
"Every time, we commit like that... that’s my team, the Wolfpack. All day we went for one goal, to win a stage in La Vuelta. We didn’t know if we could win or not, because there were 3000 metres of ascent.
"It’s not an easy sprint. I’m happy for this wonderful season continuing. It’s my first stage in La Vuelta after finishing two times second and I’m really happy with that."
There was no change to the general classification with Michał Kwiatkowski (Sky) leading Alejandro Valverde (Movistar) and Wilko Kelderman (Sunweb).
While testing in its early phases, the 178.2km stage from Mijas to Alhaurín de la Torre was one marked down for the sprinters and that is what eventuated.
Luis Angel Mate (Cofidis) and Pierre Rolland (Education First-Drapac) were again in the break but with a different assortment of companions including Jordi Simon (Burgos-BH), Antonio Molina (Caja Rural-Seguros RGA), Hector Saez (Euskadi-Murias) and Nans Peters (AG2R).
With 52km left to race, the break lost Rolland with only a 57 second lead on the peloton but Mate was happy - the mountains classification leader was riding on his local roads and looking to add to his tally.
“There’s nothing like riding home," he said before the stage. "I’m delighted to be here and I hope to do a good stage. Today is hard, with the Cat-1 Puerto del Madroño, and we’ll try to be in the front.”
The Cofidis rider had no trouble on the Puerto del Madroño, taking the maximum points before doing the same later down the road on the Puerto del Viento.
The race pace was slow and continued that way until the 42km mark, the break almost vanquished when Victor Campenaerts, his Lotto-Soudal team-mate Jelle Wallays, Lukas Postlberger (Bora-Hansgrohe) and Alexis Gougeard (AG2R) bridged across to add some much-needed action and horsepower.
As the peloton closed in and the break fell apart, Postlberger threw caution to the wind with a solo ride in the last 20km, an effort which came to an end with six kilometres left to race and where the sprint trains took over.
The race continues with Stage 4, a 161km mid-mountain stage from Vélez-Málaga to Alfacar Sierra de la Alfaguara.