At issue in the New York case are alleged "striking similarities and overt common elements" between Gaye and Sheeran's songs.
The plaintiffs are the heirs of Ed Townsend, a musician and producer who co-wrote Gaye's 1973 soul classic, who were also in court Tuesday.
"I am here for justice, protecting my father's intellectual properties," Townsend's daughter Kathryn Townsend Griffin told journalists outside the courthouse.
"As Marvin Gaye would say, 'Let's get it on,'" quipped Ben Crump, lawyer for the plaintiffs.
Sheeran's "Thinking Out Loud" shot up America's Billboard Hot 100 charts when it was released, and won Sheeran a Song of the Year prize at the Grammys in 2016.
Townsend's family has pointed out that the group Boyz II Men has performed mash-ups of the two songs, and that Sheeran has blended the songs together on stage as well.
The lawsuit, filed in 2016 - and refiled in 2017 after being rejected on procedural grounds - also names Sony.
Sheeran's team contests the allegations, saying "there are dozens if not hundreds of songs that predate and postdate" Gaye's song, "utilizing the same or similar chord progression."
"These medleys are irrelevant to any issue in the case and would be misleading [and] confuse the jury."
There have been a flood of such copyright trials in recent years, notably in 2016 when Gaye's family - who is not part of the New York lawsuit against Sheeran - successfully sued the artists Robin Thicke, Pharrell Williams, and T.I. over similarities between the song "Blurred Lines" and Gaye's "Got to Give it Up."
They were ordered to pay some $5 million in damages, in a result that surprised many in the industry including legal experts who saw many of the musical components cited as foundational musical elements largely in the public domain.