De Marcos put the hosts ahead at San Mames with a neat side-footed finish from Jon Aurtenetxe's cross in the 27th minute and Susaeta made it two with the last attack of the half as Andres Palop could only help his powerful drive into the net.
However, a grandstand finish was ensured when Athletic were reduced to 10 men as Ander Herrera was shown a second yellow card 14 minutes from time, and two minutes later Alvaro Negredo reduced the arrears from the penalty spot.
Sevilla then laid siege to the Athletic goal but were denied on a couple of occasions by Gorka Iraizoz as their winless run in the league extended to a third game.
Athletic were all but eliminated from the Europa League on Thursday night, thanks to a 3-2 defeat to Lyon, but Marcelo Bielsa kept faith with the same 11 that started that match and nearly got his reward within 60 seconds as Federico Fazio fluffed an attempted clearance, but Aritz Aduriz saw his attempted lob float just over the bar.
Jesus Navas then dragged an effort inches wide at the other end but Athletic were getting a lot of joy down their left side, and it was from there that the opener arrived as Aurtenetxe picked out De Marcos perfectly on the edge of the area, the latter's shot arrowing into the corner of the net.
Susaeta should have made it two when he headed straight at Palop from another Aurtenetxe cross a minute before the break, but he would celebrate his call-up for Spain's friendly against Panama in style moments later as he raced onto a flick-on by Aduriz and, despite getting two hands to the midfielder's volley, Palop couldn't keep it out.
Sevilla manager Michel showed his intent by introducing Baba Diawara and Jose Antonio Reyes at the start of the second half, but despite pouring forward they could not find a way past Iraizoz.
Geoffrey Kondogbia had a good long-range effort turned behind before Iraizoz produced a remarkable double save to deny Baba and Negredo 20 minutes from time.
Ander was then sent off for a handball that led to a second yellow card, and moments later Sevilla did have a route back into the game as Negredo comfortably converted from the spot after Andoni Iraola was harshly judged to have handled.
Negredo ought to have equalised eight minutes from time but instead scuffed his shot into the hands of Iraizoz as Athletic held on to move to within a point of Sevilla in mid-table.