Morecambe took the lead after 21 minutes when debutant Jordan Mustoe chased a loose ball and poked home from close range after a defensive mix-up.
The Shrimps wasted two good chances to add to their lead at the start of the second half and were made to pay as Preston levelled through Graham Cummings, who got the final touch to a 55th-minute Nicky Wroe free-kick.
Sodje fired Graham Westley's side into the lead with his first touch of the ball after 76 minutes, but the Shrimps equalised two minutes later when Richard Brodie scored from the penalty spot after a Keith Keane foul.
Paul Huntington headed Preston back in front 10 minutes from time and Sodje completed the scoring in injury time when he took advantage of a poor Andreas Arestidou clearance to slide the ball into the empty net from 30 yards.
