It took just four minutes for the scoring to be opened at Tooting and Mitcham's KNK Stadium, with Bolton Wanderers forward Jamie Thomas smashing in a free-kick from 25 yards out.
After a bright opening few minutes for Palace, Bolton capitalised on their first chance, following a late challenge by defender Roderick Collins.
Despite the initial drama of an early goal, neither side created much in the way of chances for the remainder of the opening 15 minutes.
Sullay Kaikai and Jake Gray both showed promise when running at the Bolton backline, but Palace continued to struggle for a way back into the game.
Just after the 20-minute-mark, Marouane Chamakh won Palace a free kick inside the Bolton half. It was played deep in towards Connor Dymond, who headed the ball into a dangerous position. Bolton cleared, but only as far as Dymond, allowing the skipper to thunder home a brilliant equaliser from 25 yards out.
Bolton soon retook the lead, when they strung together several neat passes to release Chris Cvetko inside the box. The Trotters' midfielder took a touch to shrug clear of Palace defence and fire low beyond Wayne Hennessey - who got a touch to the effort, but it wasn't enough to keep it out.
As the first period came to a close, Bolton added a third. Thomas tapped home his second of the afternoon, having seen his close-range effort parried back into his path by Hennessey. The two sides went in with the score at 3-1 to the visitors.
Palace managed to claw a goal back 12 minutes after the restart, following some brilliant work by Sullay Kaikai. The Eagles winger rounded the full-back, burst into the box and cut the ball back to Jake Gray, who tapped home from five yards.
With just under fifteen minutes to go, Palace were nearly back in it. Kaikai burst through on goal after a neat one-two with Sako, before being pushed over in the box by last man Alex Finney. The Bolton defender was sent off and Kaikai stepped up to take the spot kick, which was saved well by Campbell.
The home side continued to press for a way back into the game after the penalty miss, but were largely limited to shots from distance until the closing five minutes. Kaikai - who had been a threat throughout - wriggled into the box again and was hauled down, winning another penalty. This time Bakary Sako stepped up, but his attempted Panenka penalty sailed over the bar, letting ten-man Bolton off the hook again.
Incredibly, Kaikai won Palace a third penalty on 90 minutes, which was this time taken by skipper Connor Dymond. The defender succeeded where Kaikai and Sako had failed, lashing home from 12 yards to level the scores at 3-3.
Bolton's goalkeeper, Harry Campbell, was called into action twice more in the final minute, spectacularly denying Keshi Anderson and then Luke Croll, ensuring the game finished 3-3.
Palace XI: Hennessey; Johnson-Schuster (Breimyr, 45), Collins, Croll, Scales; Gray, Dymond, Kaikai, Sako; Chamakh (Anderson, 60), Bissaka.
Subs: Perntreou, George, Allassani.
Bolton XI: Campbell, Maher, Kellett, White, Finney, Perry, Campbell-Young, Cvetko (Garrett, 61), Newell, Ceberio (Griffiths, 68), Thomas.
Subs: Spooner, Jaaskelainen, Honeyball.