The midfielder provided the game's outstanding moment in the second half as he scored a wonderful curling effort from 20 yards to help give the Blaugrana a strong first-leg lead
The home side failed to pose much of a threat at the Estadio de Mendizorroza and instead the visitors attacked as Alexis Sanchez had a brilliant chance to give Barcelona the lead in the 13th minute after some fine play down the right from Dani Alves. Unfortunately the Chile international could only head straight at Urtzi after being found unmarked inside the area by his team-mate.
Alves served another enticing cross towards Sanchez just minutes later but again the attacker wasted the opportunity, this time nodding the ball wide of the Alaves goal under little pressure from either Agustin or Javier Hernandez.
Barcelona continued to threaten as the first half wore on, with Alves proving a constant torment for Manu Garcia down the right, and Iniesta coming close to opening the scoring with a low shot in the 26th minute that was parried away well by Urtzi.
Vilanova's side did finally make their dominance pay in the 40th minute when Villa smashed an unstoppable effort past Urtzi from the edge of the Alaves box after controlling Iniesta's pass following a costly slip from Agustin.
Guzman had a glorious chance to equalise for the home side early in the second half but dragged his shot wide of the right-hand post after barging his way into the Barcelona penalty area.
Barcelona immediately made Alaves pay for Guzman's miss as Iniesta curled a delicious strike in to the net to make it 2-0. Manu Garcia was guilty of dallying on the ball inside his own area, and after Cesc Fabregas dispossessed him, the ball was slipped to first Sanchez and then on to Iniesta. The Spain international didn't need a touch to set himself and instead opted to curl an arching first-time effort into the top right corner from the edge of the box.
Sanchez then thought he had increased Barcelona's lead to three shortly after Iniesta's strike, but his neat flick was wrongly ruled out for offside after some great play by Villa on the left-hand side of the Alaves penalty area.
The Blaugrana took greater control of the match following Iniesta's wonderful finish as Alaves showed little sign of coming back into the game, and went on to score a third late on through Fabregas following more outstanding play from Alves down the right.
The former Arsenal player was left with the simplest of finishes from close range as he headed Alves' cross into an empty net with Urtzi caught out of position.
Barcelona take a comfortable lead into the second leg of this Copa del Rey tie, with the return tie at Camp Nou on November 27.