Vine caught and overtook Spain's Pablo Castrillo (Movistar) with 5 km left on the climb to the end of the 175.3 km ride from Parque de la Naturaleza Sendaviva to El Ferial Larra Belagua.
The 29-year-old - mountains classification winner last year and this year's leader of the category -- also won two stages in 2022.
"Winning is so, so hard, and it's such an incredible feeling when it happens," Vine said.
"I don't think I'll ever get used to winning, because it's just unbelievably hard."
Castrillo held on to take second spot, 35 seconds behind Vine, with the Spaniard's compatriot and teammate Javier Romo finishing third.
Vingegaard (Visma-Lease a Bike) had lost the red jersey to Norway's Torstein Traeen (Bahrain Victorious) after stage six, but having begun Tuesday's stage 37 seconds off the lead, he opened a gap to Traeen on the final climb to move 26 seconds ahead in the general classification.
Following Monday's rest day, Tuesday's stage was a mostly flat ride, with one category three climb along the way before the category one finish, and any early breaks had all been quashed by the peloton.
A group, which eventually included 30 riders, made the decisive break 72km from the end, and they were allowed to get away, though the leading group was whittled down as the race wore on.
There were attacks from the breakaway, with Romo trying to get away, but when Castrillo made his move with seven kilometres remaining, the Spaniard looked set for victory, but Vine reacted and powered past the leader for another stage win.
The riders in the strung-out peloton were never going to contest the stage win, but the GC battle commenced on the final climb and Vingegaard, who had already closed the gap to Traeen by winning the previous stage, returned to where everyone expected the Dane to be.
Vingegaard was part of a small group which began passing some of the breakaway riders towards the finish, and his 11th-place finish on the stage brings an end to Traeen's time in the red jersey.
Wednesday's stage 11 is a 157.4km medium mountain stage which starts and finishes in Bilbao.
More to follow...