Former Birmingham and Preston midfielder Carter is spending a second week on trial with the Seagulls as boss Poyet weighs up a deal for the free agent.
And the 27-year-old did his chances no harm at all by opening the scoring at Bournemouth, latching onto Jamie Smith's backheel on the edge of the area and firing home.
Coach Luke Williams told the club's official website: "Darren did very well and scored a goal too.
"He got lots of the ball and you can see why he played at the very highest level."
Youngster Ryan Simmonds wrapped up a 2-0 win for Brighton in the second half.