Russian Yury Trofimov attacked in the closing stages of the 15-km climb but Landa (Astana) countered and held off the Katusha rider, who finished second two seconds off the pace.
Contador was five seconds behind Landa and one second ahead of fourth-placed Aru after controlling his closest rival in the final climb.
Aru's Astana team set the pace in the finale but it never bothered Contador, whose only goal was to thwart the young Italian as he chases a rare Giro/Tour de France double.
The last rider who achieved it was the late Marco Pantani in 1998.
Heading into the second rest day on Monday, Costa Rica's Andrey Amador (Movistar) is third overall 4:19 off the pace.
Australian Richie Porte, who had already been ruled out of contention after a disappointing time trial on Saturday, was dropped in the penultimate climb.
Team Sky's hopes now lie with Czech Leopold Konig who is fifth overall, 6:36 behind Contador while Landa is fourth (4:46).
The race concludes on May 31.
(Reporting by Julien Pretot; Editing by Mark Meadows)
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