The match at Espanyol's Cornella El Prat stadium in Barcelona was an unappealing spectacle littered with fouls and was a reminder how far the two clubs have fallen since they met in the final of the UEFA Cup in 2007.
Joan Verdu put the home side ahead from the penalty spot in the 13th minute before Sevilla midfielder Ivan Rakitic netted a 24th-minute penalty of his own after a Cristian Stuani foul on Geoffrey Kondogbia.
Sevilla were reduced to 10 men six minutes before half-time when Jose Antonio Reyes picked up a harsh second yellow card after the referee ruled he had taken a free-kick without waiting for the whistle.
Simao stole in moments after coming off the bench to nod a Mubarak Wakaso corner past Diego Lopez in the 60th minute to restore Espanyol's lead before another substitute, Alvaro Negredo, levelled for Sevilla for a second time with a 91st-minute header.
Espanyol, who sacked coach Mauricio Pochettino and replaced him with Javier Aguirre at the end of last month, are 19th on 11 points from 15 matches. Sevilla are 10th on 19 points.
Unbeaten leaders Barcelona, who have made a record start to their La Liga campaign and have 40 points from 14 matches, play at Real Betis on Sunday.
Atletico Madrid, six points behind Barca in second, host Deportivo La Coruna, also on Sunday, and Real Madrid, a further five points back in third, play at Real Valladolid on Saturday.
In the UEFA Cup final between Sevilla and Espanyol in Glasgow five years ago, Sevilla won a second straight title after a penalty shootout and two of the players who featured in the final, Sevilla's Antonio Puerta and Espanyol's Dani Jarque, have since passed away.
Fans paid an emotional tribute to the pair on Friday in the 16th and 21st minutes of the match, corresponding with their shirt numbers.