Hostile crowds
The Russian long jumper will now face competitors including Serbia's Ivana Spanovic and Germany's Malaika Mihambo in Wednesday's final. They qualified in first and second place with jumps of 6.87m and 6.82m.
Klishina has a personal best of 7.05m but has failed to make it past the seven-metre mark at an outdoor event since 2011.
Seagrave, who coached Russian tennis player Maria Sharapova as a 14-year-old, said Klishina had already been subject to out-of-competition drug testing since arriving in Rio and was unfazed by the possibility of a hostile reception in the final.
Crowds have booed Russian competitors at events including swimming, boxing and beach volleyball in Rio, fuelling what some have called a Cold War atmosphere at the Games.
Klishina went largely unnoticed at the Olympic Stadium on Tuesday night and said she was supported by her competitors.
"I don't think a positive or a negative crowd reaction is going to change the way she's going to perform," Seagrave said. "But if you're not nervous at the Olympic Games, you better have your pulse checked."