After Spaniard Landa surged clear around nine kilometres from the steep finish into Cortals d'Encamp, Italian Aru left some of his main rivals trailing to take second place, with Team Sky's Ian Boswell third.
Boswell's team mate Froome suffered a crash shortly after the start at Andorra la Vella from which the Tour de France champion never recovered and he limped over the line nearly nine minutes behind Landa.
Sky rider Geraint Thomas told reporters Briton Froome had hurt a foot, a knee and a shoulder but had decided to fight on.
Aru leads second-placed Spaniard Joaquim Rodriguez (Katusha), who helped design the stage, by 27 seconds in the general classification.
Tom Dumoulin of the Netherlands (Giant-Alpecin), who was first heading into Tuesday's rest day, is a further three seconds behind in third.
"The team was incredible today," Aru told reporters.
"This morning we agreed that Landa would go for the stage and he managed to get into the right break and went on to win what was a really difficult stage," he added.
"It was a real demonstration of strength and I’m really happy to be in the leader’s jersey.
"There’s still 10 stages to go and so we’ll take things day by day but we’ll try to defend it."
Froome's bid for a rare Tour-Vuelta double after his second triumph in France in July looks to be over and the Briton is now seven and a half minutes off the lead in 15th.
Billed as one of the toughest ever challenges in a grand tour, Wednesday's so-called Queen stage included six classified ascents and more than 5,000 metres of climbing.
There was more trouble for the Tinkoff-Saxo team when Sergio Paulinho was apparently struck by a motorcycle operated by Spanish television broadcaster RTVE.
The incident prompted owner Oleg Tinkov, already angry after a similar incident forced Peter Sagan to pull out last week, to threaten to withdraw the team from the race.
"Sergio Paulinho was hit today by TVE motorcycle and end up at hospital w(ith) 17 stitches," Tinkov wrote on his Twitter account.
"What a messy and shallow race! They pay us NO money for the race and even damage riders," he added.
(Reporting by Iain Rogers, editing by Toby Davis)
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