Aru and his Astana team made multiple efforts to shake Dumoulin (Giant-Alpecin) over the 204km stage from Roa to Riaza, but the flying Dutchman covered all Aru's surges - even putting in a small attack of his own.
Aru said he had "tried his best" after the stage.
"I wanted to isolate Dumoulin and put him in difficulties. The team collectively rode very well today," Aru added.
Aru hinted that Saturday could be the best day to overhaul Dumoulin's slim three-second lead:
"The third of these mountain stages [on Saturday] is the hardest. Three seconds is nothing.”
Friday's cobbled ascent into the stage finish Avila could also be a launchpad for an attack, but large time gaps are unlikely. Instead, time bonuses may play a more significant role.
Astana directeur sportif Stefano Zanini admitted that opportunities to put Dumoulin, who looked in control today, are running out.
"It’s going to be hard to pull back those three seconds,” Astana sports director Stefano Zanini told Cyclingnews. “Dumoulin is still in fantastic shape and he responded every time. But we still have two days left to try."