The hip-hop stars collaborated on the 2018 tune for the "Black Panther" movie soundtrack, but Yeasayer claim the pair lifted part of the song from their 2007 track "Sunrise" - and failed to credit them.
In legal papers obtained by TMZ, the New York-based bandmates allege that they had recorded a "distinctive choral performance" themselves for "Sunrise", described as featuring "male voices singing in their highest registers, with animated, pulsing vibrato".
They have accused Lamar and the Weeknd of stealing the segment and slightly modifying it with "intent to conceal the infringement", and using it up to eight different times throughout "Pray for Me".
Yeasayer insist the part is "immediately recognizable" as their work, and they are now demanding all profits from sales of the single, as well as damages and an injunction blocking further sales and airplay.
Lamar and The Weeknd have yet to respond to the allegations.