Valencia led just nine seconds into the match through Seydou Keita and were 2-0 up when Eduardo Vargas found the net 10 minutes before half-time.
But Almeria replied with two goals in as many minutes early in the second half with Oscar Diaz and Corona bringing them level for a crucial point.
The fans had barely taken their seats in the Estadio Mediterraneo when Keita fired home from close range to open the scoring.
Valencia continued to threaten as Vargas and Paco Alcacer had chances soon after, while Almeria could do no better than ambitious long-range efforts from Alex Viddal and Suso that missed the target.
The hosts were grateful to goalkeeper Esteban Suarez for keeping out Joao Pereira's close-range effort with a brilliant save in the 17th minute, and they were then unlucky not to level as Vidal brought an equally good block from Vicente Guaita in the 25th minute.
Guaita then did well to keep out Vidal's long-range effort, but moments later Almeria found themselves 2-0 down as Vargas finished from 12 yards with a low shot.
Almeria regrouped at half-time and began the second-half strongly, with Guaita making two excellent saves to deny Suso and Vidal in quick succession.
It was a warning Valencia did not heed and Almeria's fans were still celebrating Diaz's close-range finish when Corona levelled in the 54th minute.
The hosts were on top, with Guaita diverting Suso's drive around the post before Angel Trujillo's acrobatic overhead kick bounced the wrong side of the post and Suso blazed over.
Valencia were struggling to reassert their earlier dominance, but Javi Fuego went close with a header before Dani Parejo brought a fine save from Suarez from 25 yards.
A draw seemed a fair result by the finish, but it leaves Valencia down in ninth place while Almeria are hovering two points above the drop zone.