Tito Vilanova's side had plenty of possession, but a tenacious Alaves would not be broken down easily. It took the Catalans until the 40th minute to force an opening through Villa, who thumped in an effort off the bar.
Villa's strike was enough to give the Catalans a half-time lead, but the hosts almost levelled the tie early in the second half when Guzman advanced into the box only to fire wide of the target.
Vilanova's men punished Alaves less than a minute later through an Iniesta wonder goal. The midfielder found the top corner with a delicate finish from outside the area to make it 2-0 to Barca.
It should have been game over just after the hour mark when Alves put an inviting low cross into the box, but the out-stretching Villa could not connect with it.
Barca had a penalty appeal turned down as Fabregas appeared to be hacked in the box with little more than 15 minutes remaining, and had a pair of Sanchez efforts saved by Iturrioz late on, but did not extend their advantage until the final minute.
Alves supplied the cross for Fabregas to nod home at the death and give Alaves a mountain to climb in the second leg.