Dutch forward Luuk de Jong broke the deadlock in the 55th minute, after Sevilla had dominated the first half, when he raced to meet a cross from Marcos Acuna and found the net with a sidefooted volley.
Julen Lopetegui’s Europa League holders had a total of 22 shots on goal to the visitors’ two, hitting the target nine times and seeing Joan Jordan rattle the crossbar in the second half.
Rennes goalkeeper Alfred Gomis was also on form, parrying a header from De Jong in the second half, an early strike from Lucas Ocampos and tipping a vicious volley from Munir El Haddadi on to the crossbar.
While there was a sense of disbelief that Sevilla could not score more, there was also relief at earning a first win in five matches in all competitions after suffering shock defeats to Eibar and Granada in their last two La Liga outings.