Spurs headed into the WSL clash winless in their opening six games of the season, though Bristol have fared worse, losing their opening five games and conceding 28 goals in the process.
US star Morgan signed for Spurs this summer, but injuries and a lack of match fitness have hampered her opportunities for game time so far.
However, Spurs boss Karen Hills gave Morgan her first appearance off the bench during last week’s 1-1 draw at Reading – and the World Cup winner was afforded her first start in Bristol.
Spurs got off to a poor start as Chloe Logarzo opened the scoring for Bristol from the penalty spot with just their third goal of the season so far.However, Spurs were level before the break through Siri Worm. Morgan departed at half-time as she continues to build her fitness, while Ashleigh Neville put the visitors 2-1 up after 64 minutes.
Spurs looked on course for victory, but Rianna Dean was sent off with 13 minutes left for a late challenge – and that proved costly for Spurs as Ebony Salmon’s injury-time equaliser secured a point for the hosts.
The result ensures Spurs remain winless after six games, and have plenty of work to do if they are to avoid a relegation battle.