Villarreal, who were dominant throughout the game, went ahead in the 86th minute when Lo Celso brought up his first goal for the club with a scissor kick.
But the hosts' joy was short-lived after Kounde poked home a dramatic equaliser in the 95th minute following a corner.
Earlier, Villarreal went ahead in the 54th minute when Kounde sent a header into his own net but the goal was ruled out by VAR after Villarreal's Boulaye Dia was found to be offside before a cross was played into the box.
The draw meant Sevilla remain third on 65 points, four behind second-placed Barcelona. Both teams are fighting for the second spot with the league title already sealed by Real Madrid.
Villarreal, who were knocked out in the Champions League semifinals by Liverpool, are seventh on 53 points, three points away from the spots for European qualification.