Luis Milla handed the hosts the lead from the penalty spot in the 82nd minute after Joselu was fouled by Mujaid Sadick.
The visitors pressed and levelled the game in the second minute of additional time when Aketxe latched onto a rebound and fired home.
Tenerife let slip a chance to move up into the play-off places in LaLiga SmartBank, while a point lifts Déportivo up one place in the table with five games remaining.
Tenerife go close to taking lead inside two minutes
After three consecutive victories, including a 2-0 win at league-leaders Cádiz CF on Saturday, Tenerife knew a victory would lift them up into the top six.
It was the hosts, who had the first sight of goal inside two minutes. Milla played a free-kick to the edge of the area, from the right, and captain Aitor Sanz drew a good save from Dani Giménez with his first-time effort.
Giménez’s opposite number, Adrián Ortolá, was called into action under a minute later. Sabin Merino handed the ball to David Simón and the full-back raced down the right flank before seeing his low shot pushed away at the near post.
Dani Gómez, who scored both goals against Cádiz at the weekend, was denied by the ‘keeper in the 12th minute. The striker brought down Sanz’s terrific ball over the top before striking at goal on the half turn, which was saved by Giménez.
Tenerife were patient with their build up as their opponents sat in behind the ball. Milla made room for himself after collecting a pass from the right, around 25-yards out, but struck across goal and off target.
Both sides were forced to make their first substitution due to injury. Tenerife striker Gómez was replaced by Ramón Miérez in the 22nd minute, while the visitors introduced Borja Valle for Uche Agbo.
On an extremely warm afternoon on the Canary island, both teams were looking well organised and the next chance came in stoppage time. Víctor Mollejo found Merino, whose shot was bravely blocked by Álex Muñoz and caught by the ‘keeper.
Visitors on top at the start of the second-half
Déportivo were on top from the start of the second-half and Tenerife’s Ortolá was called into action on 49 minutes when he kept out Gaku Shibasaki’s shot.
Form the resulting corner, Shibasaki played it short to Símon, whose cross was headed over at the back post by an unmarked Mollejo.
The early pressure in the second-half continued by the visitors when Sabin Merino neatly flicked Shibasaki’s cross towards goal, drawing a fine low save from Ortolá.
Tenerife’s goalkeeper kept the game level on 74 minutes, once again, when substitute Christian Santos fired at goal and the shot was brilliantly tipped away by the goalkeeper.
The home side were given the chance to take the lead on 80 minutes. Muñoz’s cross from the right was heading towards Joselu, but Sadick came in over the top of the striker and fouled the Tenerife substitute.
Milla stepped up and fired the penalty straight down the middle for his fifth goal of the season and to put the hosts ahead. With time ticking, the hosts were looking to see out the remaining minutes to snatch a crucial three points.
However, Déportivo had other thoughts and equalised in the second minute of additional time. Ortolá made a great save at his near post, but the rebound went to Aketxe, who wasn’t closed down and fired the ball into the roof of the net.
Tenerife will travel to promotion-chasing UD Almería on Saturday, while Déportivo, who are no unbeaten in six games, host third-placed SD Huesca.