However, we suffered a second penalty shoot-out loss in the new format of the competition as Palace scored five out of five from the spot and Cathinka Tandberg was denied by Shae Yanez.
Earlier, we controlled the majority of possession against a Palace side happy to sit in defensively, and had 16 attempts at goal, but we struggled to carve out clear-cut chances.
We fell behind when our former striker and captain Bethany England - who else? - broke clear and finished one-on-one after 22 minutes, a lead the visitors held until Julie Blakstad's fine finish to level with 15 minutes remaining. It stayed 1-1 and Palace pocketed the bonus point via the shoot-out.
The draw leaves us sixth in the league phase with two matches remaining - Leicester City back at Brisbane Road next Wednesday (18 November, 7pm) and Ipswich Town at Colchester on Wednesday 16 December (7pm) - the top eight teams qualify for the quarter-finals.
Martin Ho made six changes to the team that started against Brighton & Hove Albion in the Barclays Women’s Super League on Sunday - Selma Panengstuen, Ella Morris, Hanna Wijk, Matilda Nilden, Kirsty Hanson and Shekiera Martinez all came into the XI. Toko Koga captained the team for the first time.
Matilda Nilden's snapshot wide was the first effort of note after 10 minutes but Palace created the next two chances, Selma Panengstuen tipped over superbly from Molly-Mae Sharpe's header but could do little as England raced onto Sharpe's pass, steadied herself left of centre and slotted into the corner.
We continued to probe away without luck against a packed Palace defence, often with five or six across the back, supported by another three.
Our best move of the half created our best chance as Signe Gaupset found Victoria Pelova, she rolled in Martinez who stepped inside one defender before firing straight at Yanez. That was on 35 minutes and six minutes later, Martinez worked space again in the box, again hitting Yanez from the right angle.
The pattern continued after the break and Martin Ho rang the changes 10 minutes into the second half - Blakstad, Drew Spence, Olivia Holdt and Tandberg all introduced.
Moments later, Koga rifled just over from 30 yards and Yanez saved comfortably from Matilda Vinberg. We just needed that spark and it arrived via one of the substitutes - Koga delivered a teasing cross from the right and Blakstad timed her run to perfection to meet it on the volley, firing across Yanez into the far corner.
There was one final chance to win it as Amanda Nilden's cross to the far post picked out Holdt... we all waited for the net to bulge as she struck from six yards - only to hit the side-netting.
With honours even, the game went to a penalty shoot-out for the extra bonus point. Palace scored five out of five with Gaupset, Spence and Blakstad replying for - however, Yanez's save from Tandberg proved decisive.
Line-ups
Spurs: Panengstuen, Morris, Koga (c), A Nilden, Wijk (Blakstad 56), Gaupset, Pelova (Spence 56), M Nilden (Holdt 56), Vinberg, Hanson (Gunning-Williams 80), Martinez (Tandberg 56). Substitutes (not used): Kop, Dijkstra, Naz, Pierre.
Crystal Palace: Yanez, Napier, Enge, Sharpe (Lloyd-Smith 65), England (c, Larkin 65), Weerden (Blanchard 65), Cosme, Nolan, Hopcroft (Tsunoda 65), Swaby, Bartrip. Substitutes (not used): Erhabor, Everett, Ladd, Goldie, Moynihan.
Match stats
Goals: Spurs - Blakstad 75; Palace - England 22.
Yellow cards: Spurs - Koga 89; Palace - Weerden 55, Napier 73, Enge 83.
Referee: Lisa Benn.
Venue: Brisbane Road, Leyton Orient FC.
Attendance: 531.
Weather: 9 degrees at kick-off.
Official teamsheet
Penalty shoot-out