Palace were promoted as champions from South East One last season, unbeaten, with 20 wins from 22.
They certainly pushed Spurs all the way at Bromley FC, but Spurs held on thanks to Bianca Baptiste's early strike and a penalty save from Toni-Anne Wayne.
"I thought the girls were fantastic," said manager Karen Hills. "We're happy with the three points, we dug deep and it wasn't the best performance, but one of those ugly games you need to win and we ground out the result."
Spurs Ladies are straight back into action this week with a trip to QPR at Uxbridge FC in the FAWPL on Wednesday night (7.45pm).
CRYSTAL PALACE 0-1 SPURS LADIES
FA Women's Premier League South
Report by Khalid Karimullah at Bromley FC, Hayes Lane
Photographs - with thanks to Wu's Photography
Tottenham Hotspur Ladies took home three points from Palace in dramatic fashion on Sunday.
Spurs were quickly into their stride. Bianca Baptiste's cross just evaded Wendy Martin and the same player found Riana Soobadoo, but her effort was comfortable for Channelle Yardley.
Baptiste struck what turned out to be the winner in spectacular style after eight minutes. Gathering possession on half-way, she made a lung-busting run through the hosts' half before finishing low across Yardley.
Below: Toni-Anne Wayne produces a big penalty save at Palace - photo: Wu's Photography
Palace started to get a foot in the game but were denied by Martin on defensive duty and Renee Hector. Baptiste's lob then produced a fine save from Yardley and Fran Ali fired wide for Palace.
The game continued to ebb and flow and four minutes before the break, Hector was penalised for a trip on Elli Bailes in the penalty area. Pamela McRoberts stepped up but Toni-Anne Wayne guessed right and turned the spot-kick away.
As expected, Palace came out strongly in the second half. Bryan was denied by Hector and the same player fired inches wide. Hector was called into even more decisive action later, getting back on the goalline to head away Bryan's lob, a match-winning effort.
At the other end, Martin was denied on the line by McRoberts and Kelley Blanchflower hit the woodwork late on.
Spurs Ladies: Toni-Anne Wayne, Lucia Leon, Jenna Schillaci, Renee Hector, Leah Rawle (Eartha Pond 68), Josie Green, Sophie McLean, Riana Soobadoo, Bianca Baptiste, Wendy Martin, Nikita Whinnett (Kelley Blanchflower 80). Subs (unused): Megen Lynch, Alex Keown.