Colombian Johan Esteban Chaves remains third, a further 20 sec behind Froome, having finished the stage 47 seconds ahead of Froome after riding most of the stage with the Briton.
Quintana and Froome had completed the last two stages together but it quickly became clear that Sunday's race from Sabinanigo to Sallent de Gallego would be different.
Quintana and Spaniard Alberto Contador attempted various early attacks before forming a breakaway group within the first 10km of the 118.5 km stage.
Froome was left in the peloton with Chaves and their group kept slipping further behind the breakaway.
Three-time Tour of Spain winner Contador eventually trailed off towards the finish, coming home 34 seconds behind Brambilla in sixth place.
"We knew it was a short stage, so at the start of the day everyone wanted to attack," Brambilla told reporters. "We were with the red jersey within the breakaway, so we weren't sure, but I knew that I was in good shape."
"I started to believe in the victory 10 kilometres from the finish. I saw Contador was starting to fade and I had to follow Nairo. I knew that he was looking for time and if I sat in it was general classification for Quintana and the stage for me."
Monday's stage is a 156 km ride from Alcaniz to Peniscola ahead of the second and final rest day. The Tour ends on Sept. 11 in Madrid.
(Reporting by Richard Martin; Editing by Ken Ferris)
