Kerys Harrop gave Spurs the lead after just 11 minutes before Inessa Kaagman levelled the sides from the penalty spot on 33 minutes.
Hope Powell's Brighton held on until the hour mark when Angela Addison gave Spurs the lead before Morgan sealed the deal with an 84th minute penalty.
It was a day of firsts with Harrop's free kick in the first-half marking her first goal for the club and the win was also the first the team has secured under new coach Rehanne Skinner.
Skinner joined the club from the England national team set up after Karen Hills and Juan Amoros were fired in November.
Spurs were penalised on 33 minutes when Alanna Kennedy attempted an overhead kick to clear the ball but instead kicked Aileen Whelan in the head. Kaagman stepped up and converted the penalty.
Addison broke through for Spurs after 63 minutes when she went on a darting run behind the Brighton defence. With just Rebecca Spencer to beat she slotted the ball into the net.
The goal is Morgan's first for Spurs and her first since giving birth to her daughter seven months ago. The two-time World Cup winner joined the north London side in September and made her first appearance last month.