Jess Cheeseman and prolific striker Wendy Martin, back from injury, scored two goals each as Spurs led 3-1 and then 4-2 before the home side recovered to take a share of the points.
"I was glad to hear the final whistle, to be honest," admitted manager Karen Hills. "I was a nervous wreck at the end of the game.
"We should have won the game but couldn't hold onto the lead and that ultimately cost us the three points, but it's great to get the first point on the board."
The ladies return to league action against Colchester at Harlow Town FC this Sunday, September 16, kick-off 2pm.
Yeovil 4-4 Tottenham Hotspur Ladies
After a long trip to Somerset, the ladies found themselves 1-0 down early in the game when Laura Bray beat stand-in goalkeeper Chloe Burr.
Spurs dominated for the next 30 minutes and forged into a 3-1 lead.
Jess Cheeseman levelled with a fine strike, breaking from midfield, beating three players and shooting low into the corner.
The same player repeated the trick to fire Spurs ahead, this time lashing into the top corner.
Last season's top-scorer Wendy Martin marked her return after a knee injury by making it 3-1, a well-worked goal with Bianca Baptiste delivering from the right. However, Yeovil responded just before the break to make it 3-2.
The two-goal lead was soon restored after excellent work down the left from Siobhan Wilson, who cut inside and drove the ball across goal for Wendy to tap home her second for 4-2.
Yeovil piled on the pressure though and goals from Grace Rapp and Jodi Cornwall made it a final 4-4 scoreline.
Karen added: "It was one of those days where you didn't know whcih way the game would go.
"Both teams looked good in patches and then switched off in others.
"Leading 4-2 in the second half, I thought we'd hold on, but lack of concentration let Yeovil back into the game."
Spurs Ladies: Burr, Heath, Pittuck, Downie, Cheeseman, Smith (Mustaya, 65) Malony, Martin, Golding, Baptiste, Wilson (Thompson, 80).