The goal came with three minutes to go with a header from Bailey Wright.
In the other tie the Shrimps gained their first points and did the Lilywhites a favour in their 2-1 victory over previously unbeaten Carlisle.
Final Group Placings:
1-Preston NE - Pld 3 - 6 pts - GD 0
2-Tranmere - Pld 3 - 4 pts - GD +2
3-Carlisle U. - Pld 3 - 4 pts - GD +1
4-Morecambe - Pld 3 - 3 pts - GD -3