Aleix Vidal opened the scoring just before the break at the Ramon Sanchez Pizjuan but Los Che nicked a point through Lucas Orban - despite the dismissal of Rodrigo
Aleix Vidal's strike just before the break looked set to earn the Rojiblancos all three points points from their Primera Division opener.
However, Valencia never stopped fighting, even after the dismissal of Rodrigo midway through the second half, and were rewarded for their persistence with just over a minute of normal time remaining when Orban bundled the ball home.
The defender's effort may have been both ugly and fortuitous, with the ball having ricocheted into the Argentine's path before he chested it home, but the visitors would argue that they deserved their slice of luck.
Indeed, Valencia were desperately lucky to have not opened the scoring when Pablo Piatti was put in on goal with just nine minutes gone.
However, the midfielder's low strike cruelly struck both posts without ever going over the line, much to the relief of Beto in the Sevilla goal.
Both sides subsequently struggled to create any clear-cut openings until the hosts broke the deadlock just before the break.
Carlos Bacca eluded two players on the left-hand side before slipping the ball inside to Vidal. The midfielder's first effort struck Beto's chest, but he made no mistake with the rebound to send the Sanchez Pizjuan wild.
Bacca's pace continued to cause Valencia problems in the second half and the striker was also involved in what should have been a second goal for Sevilla in the 66th minute. However, Vitolo fired wide with the goal at his mercy.
Still, it did not seem as if Sevilla would be punished for their profligacy, as just moments later, Valencia summer signing Rodrigo was shown a straight red card for elbowing Vitolo just moments after coming on as a substitute.
Valencia kept pressing, though, and, after a well-worked corner on the left-hand side, the ball dropped for Orban, who directed it over the line with his chest to earn his side the unlikeliest of draws.