Having seen rivals Barcelona close the gap at the top to a point with a 3-1 win over Granada on Saturday, Real initially looked like matching them after Cristiano Ronaldo's second-half penalty.
Ronaldo's spot-kick gave Carlo Ancelotti's men the breakthrough following a foul on the forward inside the area from Eric Bailly early in the second period.
Moreno's effort was the first goal Real conceded since the 4-0 defeat at the start of last month to city rivals Atletico Madrid - who also dropped points on Sunday with a draw at Sevilla.
Amid a low-key opening, the visitors threatened first as Iker Casillas denied Moreno one-on-one before Dani Carvajal was forced to clear Moises Gomez's follow-up off the line.
Karim Benzema headed Toni Kroos' delivery off target before Pepe looped a header over from the German's free-kick after 22 minutes as Real began to assert their quality.
While clear-cut chances were few and far between in the opening half hour, Marcelo's dangerous cross almost beat Sergio Asenjo at his far post before Raphael Varane headed wide from a corner.
And Ronaldo duly kept his composure to slot home his 30th league goal of the season - beating Asenjo comfortably to the goalkeeper's left.
The Portuguese came close to doubling his tally when a goal-bound free-kick was deflected off target by the Villarreal wall before Real were pegged back by Moreno's impressive strike midway through the second half.
Ronaldo looked on course to single-handedly seal maximum points as he broke free down the left only to be thwarted by Asenjo before seeing a header palmed away by the visiting goalkeeper.
Bailly was perhaps fortunate not to concede another penalty as he appeared to shove Hernandez late on, only for referee Jose Gonzalez to wave away the Mexican's furious appeals as an under-par Real failed to find a winner.
It could have been worse for Real however, had Luciano Vietto maintained his balance when free on goal instead of stumbling at the crucial moment.
