Celta goalkeeper Yoel Rodriguez was the busier of the two custodians, including making three important saves late on, but the home side were not without their opportunities either as the spoils were shared.
Promoted Villarreal had won three and drawn the other of their four matches since returning to the top flight, with only Real Madrid taking points off the Yellow Submarine so far, and they looked in confident mood early on with Jonathan Pereira not afraid to try his luck.
In the opening 25 minutes he went close with two efforts while also being denied by Yoel's feet.
At the other end Alex Lopez and Santi Mina sought to give Celta the lead but were unable to find the target as the first period finished in stalemate despite both sides being eager to get forward.
After the break it was Villarreal who looked the more threatening and former Real Betis striker Pereira failed to make the most of another chance in the 65th minute.
The visitors pushed hard for what could have been the winning goal as full-time approached but they found Yoel in unbeatable form.
The 25-year-old blocked a close-range shot from Javier Aquino in the 81st minute and then saved superbly from Pina soon after.
Yoel continued to frustrate Villarreal as he produced another stop to keep out Hernan Perez's effort with three minutes left to ensure his side of a point, taking them on to six for the season, still five behind their opponents.