Spain playmaker Iniesta netted for the holders in the 10th minute at their Nou Camp arena but in the face of near-constant pressure on their goal the Czech side somehow managed to hold firm until Villa scored eight minutes from time.
World Player of the Year Lionel Messi had a frustrating night, twice hitting the post and several times being denied by last-ditch tackles.
The Argentine, competition top scorer the past three seasons, curled a long-range free kick on to the inside of an upright in first-half stoppage time and flicked the ball on to the post after a dazzling run early in the second half.
Iniesta’s goal came after a trademark quickfire passing move that left the visiting defenders in disarray.
He twice exchanged passes with Messi before dinking the ball around his marker and sidefooting narrowly inside the near post from close range.
Villa made sure of the three points when he followed up after a Messi effort and swept the ball high into the net.
Plzen, the Czech champions who are making their first appearance in Europe’s elite club competition, barely threatened the home goal.
With three of six games played, Barca and AC Milan both have seven points after the Italian side beat BATE Borisov of Belarus 2-0. Plzen and BATE, who lost 5-0 at home to Barca, each have one point.