The new world record signing was joined on the scoresheet by his predecessor, Cristiano Ronaldo, as the visitors came from a goal behind to take the lead against their newly-promoted hosts.
But Villarreal - who, like Real, came into the game with a perfect record of three wins out of three - almost stole the show from the two megastars with a fluid team performance more akin to their 2006 heyday as a Champions League semi-finalist side than a side who spent last term in the second tier.
Cani deservedly put them ahead in the first half, slotting home after the shaky Real back line struggled to handle the lively pair of Bruno and Jonathan Pereira, before former Barcelona prospect Giovani dos Santos equalised with 20 minutes remaining to give an entertaining encounter the right result, all things considered.
Playing in a three-man attacking midfield with Ronaldo and Isco to support lone striker Karim Benzema, Bale sped into the area, showing great upper body strength to get the better of Mario Gaspar, and clipped a Dani Carvajal cross into the net with his right foot before being mobbed by his new team-mates.
The Welshman was withdrawn after 61 minutes and replaced with Angel di Maria, having been a doubt to start the game during the week as he continues to edge towards a return to full fitness.
Ronaldo netted a bizarre goal to put Real ahead in the 64th minute when his own shot cannoned back off a defender onto his leg and ricocheted into the net.
It was hard on an impressive Villarreal side, who had been denied by a string of brilliant saves from Diego Lopez, but they were level in the 70th minute when Dos Santos lashed in a shot that crept into the net off the Real keeper.
The two sides now sit in third and fourth behind Barcelona and Atletico Madrid - who were able to keep a 100% league record on match day four with wins on Saturday.