World number three Alcaraz, 20, missed a month prior to Madrid with a forearm issue
Victor Languardia hit the bar in the first half as Alaves dominated throughout.
However, it was Hernandez, on loan from Atletico, who had the hosts' best chance to seal all three points when his low drive was turned behind Moya two minutes from time.
A point moves Atletico a point ahead of Real Sociedad in fourth, but Diego Simeone's men could lose further ground on the top three with Real Madrid, Sevilla and Barcelona all in action on Sunday.
And a poor day for Atletico was rounded off by muscle injuries suffered by Jose Maria Gimenez and Angel Correa which make them serious doubts for Wednesday's Copa del Rey semi-final first leg at home to Barcelona.
"Taking a point is the best thing given what we saw on the field," said Simeone.
"It was a poor game in general and we have to improve rapidly to be better in the next game."
In a sign of what was to come, Alaves started brightly and Moya was called into action as early as the seventh minute when he saved smartly from Ibai Gomez.
Languardia was then unfortunate as his towering header came back off the underside of the bar and from the rebound Deyverson and Manu Garcia got in each other's way as they combined to send the rebound over.
Gimenez left the field in tears early in the second period after tearing a thigh muscle.
However, Atletico did have one great chance to steal the win when Nico Gaitan was left one-on-one with Fernando Pacheco, but was dispossessed as he tried to round the 'keeper 15 minutes from time.
With Correa also hobbling and Simeone having made all three of his substitutions, Atletico were effectively left with 10 men for the final stages.
And Alaves nearly took advantage thanks to an Atletico player as Hernandez bombed forward from left-back, but he chose to shoot with Deyverson waiting for a cut-back and Moya stood tall to deflect the ball wide.
An at times bad-tempered encounter ended on a sour note as Deyverson and Atletico defender Diego Godin spat on each other after clashing deep into stoppage time.
Earlier, sixth-placed Villarreal moved to within two points of Atletico thanks to a 2-0 win over rock bottom Granada to register their first victory of 2017.
Both goals came from set-pieces as Alvaro Gonzalez's knockdown was turned home by captain Bruno Soriano just before half-time.
And Gonzalez then got his first goal for the club by stabbing home whilst lying prone on the ground 17 minutes from time.
World number three Alcaraz, 20, missed a month prior to Madrid with a forearm issue
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