A Primera Division meeting between two of the league's in-form teams promised much and sparked quickly into life with Alberto Moreno putting the hosts ahead inside five minutes before Susaeta capitalised on an error in the Sevilla defence to level.
Susaeta was presented with the chance to put Athletic ahead from the spot moments before the interval but Beto was equal to his effort, making a good low save.
The stalemate extends Sevilla's unbeaten run in all competitions to eight games and sees them climb a place to seventh, while Athletic stay fourth after seeing their run of three straight La Liga wins brought to an end.
The match got of to a flying start with two goals inside the opening six minutes.
The hosts drew first blood when Jose Antonio Reyes's short corner was helped on by Carlos Bacca to Moreno on the edge of the box, the midfielder ghosting past a defender before firing in powerfully off the left-hand upright.
Sevilla's fans were still celebrating when they saw their team pegged back just two minutes later courtesy of a defensive howler.
Juan Cala's header back to his goalkeeper lacked pace and Gaizka Toquero nipped in to take the ball away from the sprawling Beto before centring for Susaeta to tap in from a yard.
Sevilla almost restored their lead from another corner on 26 minutes when Reyes' delivery was met by the head of Federico Fazio but Gorka Iraizoz made a good save.
But it was the visitors who should have been ahead at the break after they were awarded a penalty when Bacca handled the ball in the box.
Susaeta stepped up to take the spot-kick but Beto guessed correctly to make the save in the left corner.
The second half failed to live up to the excitement of the first with both defences comfortably on top.
The closest either side came to adding to the scoring after the break came when Athletic midfielder Ander Herrera took aim from distance but Beto was in the right place to make the save.