The Swiss GreenEdge rider had led Euskatel’s Sanchez by 1:30 going into the seventh and final stage and there was no change to the podium places in the GC as France’s Julien Simon of Saur Sojasun won a bunch sprint from Francesco Gavazzi (Astana) and Damiano Cunego (Lampre ISD) respectively.
It was Simon's second win in Catalunya, having taken stage five on Friday.
Sanchez tried to make a break on the final climb but he was unable to prevent the mass sprint and, ultimately, victory for Albasini.
Belgium's Jurgen Van den Broeck (Lotto Belisol) was third overall, with Irishman Daniel Martin (Garmin Barracuda) fourth.
"I need to thank the team for the work that they've done throughout the week," Albasini said after his biggest career win. "This is an important win for me personally and for the team. It would have been impossible without them.
"There was really no moment today when we were under terrible pressure. Those moments came earlier in the week.
"Today, we observed the different objectives of the other teams. When Garmin made their interests known, we let them ride on the front and took a secondary role.
"I had Daryl [Impey] with me on the final climb. He has been by my side throughout the entire week."