Roglic had lost the red jersey to Australian Ben O'Connor after stage six but has since chipped away at the lead before reclaiming it with an impressive performance in the mountains of the La Rioja province.
"I had some really nice memories from this climb and I didn’t miss this opportunity, I’m happy," Roglic said.
While a leading group maintained a narrow lead over the peloton for most of the race, none attempted a breakaway before the 11 km climb leading up to the finish line at Alto de Moncalvillo.
Roglic saw an opportunity halfway through the demanding ascent and seized it, never looking back. He crossed the finish line alone, 46 seconds ahead of Frenchman David Gaudu, who took second place. Denmark’s Mattias Skjelmose finished third.
O'Connor, knowing his lead was in danger, tried to keep up but finished 12th. Roglic now has a one-minute and 54-second overall lead over O'Connor.
"I was a bit broken at the end. I actually felt pretty good until halfway," O'Connor said.
"I wasn't really surprised, but I didn't expect myself to be so bad at the end. I was a bit average, to be honest. But that's just the reality."