Tomasz Kuszczak was handed a rare start in goal for United, while Cristiano Ronaldo shook off a knock to feature for Sir Alex Ferguson's side.
The opening minutes of the game saw little in the way of goalmouth action, although Wayne Rooney did have the ball in the net, but an offside flag cut any celebrations off before they had started.
Seventeen minutes in Villarreal knocked the ball around well and the attack ended with Santi Cazorla testing Kuszczak with a stinging drive from 25 yards out.
United took until ten minutes to go to half-time before they forged a meaningful opening, with Ronaldo teeing up Darren Fletcher, but his shot from the edge of the area was straight into the gloves of Diego Lopez.
Four minutes before the break Rooney laid the ball back into the path of the arriving Ronaldo and his deflected drive from 30 yards was tipped superbly onto the crossbar by the alert Lopez.
Ronaldo's low 25-yard free-kick then forced a save from Lopez as United ended the first half in the ascendancy.
Early in the second period Ronaldo broke away down the right and fired in a crisp, low shot which Lopez parried. Rooney arrived and fell on the floor looking for a penalty and was lucky to escape a caution.
That was the only clear opening for much of a disappointing second half, but United finally came close to breaking the deadlock ten minutes from time.
Rooney got clear down the left and his deflected cross was about to drop in under the crossbar before Joan Capdevila made a superb headed clearance.
However, Spain left-back Capdevila blotted his copybook soon after when he was shown a somewhat harsh red card for a late lunge on Ronaldo.
The closing minutes were surprisingly quiet as neither side seemed to have the necessary intent to find a winner, but both teams celebrated a place in the last 16 when the final whistle sounded.