Daniel Wass orchestrated the first shot in anger, but his effort from outside the box glided wide after four minutes.
Atleti grew slowly in the game, but Valencia were showing the earlier promise to clinching the three points.
The Danish defender, Wass, was in the thick of things again, but failed to get on the end of a cross from Rodrigo.
Then Gabriel Paulista followed seconds later, assisting Rodrigo to have a crack at goal which narrowly missed goal.
Diego Costa worked a bit of magic and managed to create their first effort on goal which Neto dealt with quite comfortably.
On 26 minutes, Angel Correa gave the newly-crowned UEFA Super Cup winners the lead with a smart finish after beating the offside trap.
Costa quickly pressed to increase their tally, but solid goalkeeping from Neto was on hand to stop him after 34 minutes.
On 50 minutes, Valencia tried to get back in quickly but a cross-field delivery from Dani Parejo failed to find any teammate in the box.
Five minutes later, the hosts were level. A left-footed shot from Rodrigo inside the box gave them a chance to stage a come back victory.
After 63 minutes, Atletico brought on Vitolo for Thomas Lemar to offer a different offensive dimension.
Still not finding a breakthrough, Diego Simeone made another offensive change with the arrival of Gelson Martins for his league debut, replacing star man Antoine Griezmann.
This took place, while Valencia threatened to go regain control when Paulista send a header crashing the right-side post.
It was Atleti looking to end strong, as Stefan Savic missed an inviting chance following a cross from Koke after a corner kick on 80 minutes.
But the home side quickly responded with Michy Batshuayi assisting Wass with another chance to score but the effort was saved.
In added time, Kevin Gameiro came with the final effort on goal for Atleti but good goalkeeping again spared the blushes for Simeon’s men who shared the spoils.