The best early chance fell to Brighton but Glenn Murray headed wide, while at the other end Michel Kuipers saved well from Craig Curran.
Tranmere went ahead after 35 minutes with Edds wrong-footing Kuipers to net from a pass by Ian Thomas-Moore. It needed a fine save by Kuipers from a Zoumana Bakayogo volley to prevent the hosts doubling their lead five minutes after the break.
Then Glenn Murray somehow missed the target from point-blank range from a cross by Gavin Hoyte soon afterwards.
Tranmere made it 2-0 after 66 minutes with a great left-foot strike from the edge of the box by Welsh which gave Kuipers no chance.
Glenn Murray pulled a goal back for from the penalty spot on 77 minutes after he was impeded by keeper Martin but Murray was dismissed three minutes later for a second yellow card.