Spaniard Valverde beat Team Sky’s Michal Kwiatkowski of Poland in the final stretch, with Quick-Step Floors’ Laurens De Plus of Belgium completing the podium.
Kwiatkowski, however, took the race lead and with it the red jersey, 14 seconds clear of Valverde in second.
A break of seven riders got away almost from the outset when Alexis Gougeard, Thomas De Gendt, Pierre Rolland, Pablo Torres, Jonathan Lastras, Luis Angel Mate and Hector Saez went ahead in the first two kilometres.
By the time the seven approached the summit of the Puerto de Ojen – just 5km later – they had created a two-and-a-half minute lead over the peloton.
The breakaway group rode at a consistent pace at the head of affairs and held the peloton off by three minutes with 92km left.
As the break hit the base of the Alto de Guadalhorce, a 7.1km climb with a three per cent gradient, their lead grew to over four minutes.
With 56km remaining, De Gendt began dropping back from his fellow escapees as he slowly looked to rejoin the peloton.
The breakaway held a two-minute-10-second lead with 50km left as Bora-Hansgrohe and BMC Racing led the peloton.
With 30km to go, Team Sky and Movistar pinned themselves at the head of the peloton to pursue the breakaway group.
Just a couple of kilometres later Saez, Mate, Lastra and Torres were reeled in as Gougeard and Rollan held a 49-second lead. Gougeard was dropped with 20km left, as Rollan soloed ahead.
His lead was to no avail and he too got caught a mere kilometre later. Team Sky continued to set the pace, which strung out the peloton.
Astana Pro later joined Team Sky at the head of the peloton on the run-in to the base of the Alto de Guadalhorce, a 7.1km climb with a 2.8 per cent gradient.
Race leader Rohan Dennis from BMC Racing had dropped back to over five minutes behind the peloton and was certain to lose his red jersey.
Salvatore Puccio set a relentless pace at the head of the peloton for Team Sky over the last five kilometres as the leading group began to reduce in numbers.
De Plus broke away from the peloton and soloed ahead, but he was reeled back in heading into the final kilometre.
Kwiatkowski attacked first within the last kilometre, but Valverde’s experience came through as his attack in the final few hundred metres ensured he did enough to overtake Kwiatkowski and claim victory.
Stage three tomorrow will comprise a 178.2km race from Mijas to Alhaurín de la Torre.