With the bonuses added to the win, Alaphilippe (Quick-Step Floors) holds a four-second overall lead on Roglic (LottoNL-Jumbo), with Pello Bilbao (Astana) third going into the 153km third stage from Zarautz to Bermeo.
“I am very happy, especially as I got sick after Milano-Sanremo and had to rest before returning to training," Alaphilippe said. "I was very motivated after this small setback, so I worked hard to be back at my best.
"The plan was to take a stage here and even though we did a recon of the final climb yesterday and on paper it suited me, I didn’t know how my legs would react following that break.
"I was focused, smart and strong, I worked well together with Roglic, who too was very strong, and in the end, I bided my time before powering to this nice win.
"A big thanks to my team for protecting me today and to the amazing crowds, who cheered for us before the start and at the finish.”
A breakaway of four riders opened the race but was unable to truly shake free of the peloton and after dangling out front for the majority of the stage were swept up with 26km to go.
The peloton drove hard to the base of the final climb with Roglic forcing a split along with Alaphilippe and Nairo Quintana (Movistar).
Roglic and Alaphilippe pushed hard forcing Quintana to drop off with a single kilometre to go with the pair then battling to the finish.