The midfield duo struck in the second half after Susaeta's early opener to put the Basques within one win of a place in the qualifying round for Europe's top competition
Susaeta put the home side in control by scoring directly from a corner before Iker Muniain and Ander Herrera settled matters against Unai Emery's side, who had Diogo Figueiras sent off in the second half.
The result means Athletic need just one win from their final three games to seal fourth spot in La Liga, while Sevilla - who rested some key players for the clash - will now turn their attention to the Europa League semi-final second leg with Valencia on Thursday.
It took Athletic just five minutes to break the deadlock, with a Susaeta corner creeping inside the near post after just five minutes following uncertainty in the Sevilla defensive ranks.
With a precious Champions League spot up for grabs, it was a fiesty first half at San Mames, with four players all finding themselves in the referee's notebook as each side scrapped for supremacy.
Athletic were the more comfortable team looking the more likely to find the second goal and they duly obliged just after half-time.
Valverde's men broke down the right wing and Andoni Iraola crossed to the far post for Muniain, who ghosted in unmarked to volley home with his right foot.
Muniain was booked for dissent just 10 minutes later as Daniel Carrico was lucky to escape a second yellow card for a trip on Ander Herrera, and the stoppage prompted Emery to call on Ivan Rakitic to try to find a way back into the match.
The midfielder came close a few minutes after his introduction as he fired a half volley wide of the left-hand post, but the task soon became insurmountable as Diego Figueiras was sent off for a second booking.
And just a minute later, the match was settled, as Iraola bent in another good cross from the right to allow Ander Herrera to head low into the corner for his fourth Liga goal of the season.
Sevilla responded well, with substitute Jairo touching the ball into the path of Kevin Gameiro to sweep into the corner, but in the end it was too little too late for the visitors as Athletic moved to within a victory of the Champions League playoff round.