In a frantic encounter at Stade Marcel-Deflandre, the home side survived a late scare to progress into a major international final for the first time, Gregory Alldritt's 51st-minute try proving decisive.
Two-time European Challenge Cup winner Sale took the lead, referee Nigel Owens awarding the visitors a penalty try after Victor Vito brought the maul down.
La Rochelle soon levelled through a penalty try of its own, however, with the TMO (television match official) deeming that Denny Solomona's high tackle on Vincent Rattez was also worthy of a yellow card.
The Top 14 side was ahead in the 26th minute when Kini Murimurivalu raced through a gap in Sale's lines, although England winger Chris Ashton, who was back from the calf injury that cut short his Six Nations, ensured the scores were level at 17-17 at the interval.
But La Rochelle would be in front again when Ihaia West teed up Alldritt to score, and although AJ MacGinty pulled Sale within four points with a composed penalty conversion, the visitor could not force itself over as, despite Jules Favre's late yellow card reducing its numbers, the host held firm to book a final clash with either Clermont or Harlequins.