The result wasn't enough to keep Gordon Strachan's side in Europe though as they still finished at the foot of the group despite the victory.
The Yellow Submarine and Manchester United qualify for the last 16 of the Champions League while third-placed Aalborg move into the UEFA Cup.
The Bhoys started well with Scott Brown's cross finding Shaun Maloney whose shot was saved by Viera.
When play swung to the other end, Franco tested Artur Boruc with a fierce shot and Mati Fernandez played a low cross towards the same player who fired wide of the target.
Celtic opened the scoring in the 14th minute when Mark Wilson's cross bamboozled Viera allowing Maloney to head into an empty net.
When Villarreal tried to hit back Edmilson headed a 28th-minute corner wide, but the visitors' cause wasn't helped seven minutes later when they were reduced to ten men.
Swiss referee Claudio Circhetta consulted his assistant before showing Franco a red card for violent conduct following an altercation with Stephen Caldwell.
Aiden McGeady grabbed Celtic's second goal on the stroke of half-time with a superb individual effort. He picked up the ball near the halfway line and ran unchallenged before firing home from 18 yards out.
In the second half, Celtic were unfortunate not to add a third goal as Georgios Samaras almost got on the end of Maloney's cross before Shunsuke Nakamura had a long-range effort saved by Viera.
But Strachan's side had already done more than enough to clinch their first win in the group in their final game in Europe this season.