Manuel Pellegrini's side, currently sixth in La Liga after taking four points from their first two games of the season, were cautious throughout but almost snatched a dramatic win when Guillermo Franco hit the post with a sublime back-heel.
The Yellow Submarine also played out two 0-0 draws against United in the group stage of the 2005-06 competition.
Ferguson's side were eliminated after finishing at the bottom of the group then, while Villarreal went on to reach the semi-finals, but with Celtic and Aalborg also in their group this season, Ferguson's side will surely not suffer the same fate this time.
Villarreal, second behind champions Real Madrid last season, made a slow start at Old Trafford and goalkeeper Diego Lopez was particularly sloppy.
In the ninth minute he came for Owen Hargreaves' corner only to miss it but Rio Ferdinand was unable to divert the ball goalwards.
Six minutes later Nani almost caught the shot-stopper out with a rasping 30-yard drive and, midway through the first half, Darren Fletcher and Nani combined well to set up Park, but the South Korean's shot was deflected for a corner by Edmilson.
On the half-hour mark Lopez made his best save of the night to keep Carlos Tevez's fierce drive out and, before half-time, United's appeals for a penalty were turned away by the referee when Park went down under Joan Capdevila's challenge.
The visitors improved after the break and in the 61st minute they almost took the lead when Lopez Ruano Angel crossed for Franco. He instinctively back-heeled the ball on to the inside of the post and, luckily for United, it bounced straight in to Edwin van der Sar's arms.
United pressed for a winner in the closing stages and Ronaldo and Wayne Rooney combined to set up Tevez, whose shot was destined for the back of the net until Gonzalo Javier Rodriguez made a superb last-ditch clearance.
With seven minutes left Ronaldo crossed for Jonny Evans to head against the post when he should really have found the net, as the match eventually ended in a stalemate.