Bailey scored with 17 minutes left, cancelling out a wonder strike by Giovanni McGregor, at Selhurst Park.
It proved to be a thorough examination of Blues mettle as much as their ability on an afternoon when lashing rain pockmarked proceedings.
Palace fielded a more knowing side, including three transfer deadline signings Gary Cahill, Victor Camarasa and James McCarthy.
By contrast, Blues back four were all teenagers including debutant Nico Gordon, 17, at right-back, who performed impressively.
Blues stayed in there when the going was difficult, and after levelling they could actually have come away from south London with a victory.
Blues showed commendable resolve and determination in the first-half.
It was a story of important positioning and defending to hold the score level.
Palace threatened first when James Daly went to shoot inside the area only for Ryan Burke to slide in with a block.
Connal Trueman then parried away Daly's attempt from the left, just outside the area, after Blues lost possession carelessly.
Bailey capitalised on a loose pass from the Palace right to dribble towards the D and create a shooting angle, only for his low shot to be blocked by an attentive Sam Woods.
Blues then enjoyed a period of good possession, calmly and confidently moving the ball around the pitch.
But Palace came again at Blues and for a sustained spell forced the visitors to dig deep.
There were shots for a penalty when Geraldo Bajrami stopped McGregor in his tracks with a tackle near the byline and moments later his centre-half partner Joe Redmond was alive to danger when he scooted across to shepherd Daly away as he tried to tee himself up in the area.
In the 27th minute, after a ball was clipped back in from a corner, Bajrami acrobatically hooked a downward header by Camarasa off the line after the Spaniard guided his effort past a wrong-footed Trueman.
Next it was Redmond's turn to get in the way and sidefoot on the volley away an attempt from inside the area by McCarthy.
Palace gradually increased the pressure as the first period came to a close and Blues commitment and diligence could not be faulted, showed when Jude Bellingham dropped back across and in to get away a dangerous cross from Brandon Pierrick after Palace opened them up on the left.
Blues might have gone ahead inside a minute of the second-half starting, when a move down the right was well worked for a switch to the other flank.
Ryan Burke galloped on and hit in a low, dangerous cross that fizzed along the edge of the six-yard box before being well dealt with, safety first, by Woods booting it away.
Promptly, in the next attack, Palace took the lead. And it was a sumptuous strike, from McGregor.
He got the ball on the left-hand edge of Blues area and shaped onto his right foot to then arch a curving shot into the opposite top corner, beyond the full-stretch dive of Trueman.
Blues brought on Josh Andrews in the 63rd minute and paired him up top with Spanish trialist Dani Ruiz; Bailey moved out to wide right.
Trueman came to the rescue with a double save once Daly sent through Pierrick with a defence-splitting pass.
With Nico Gordon snapping at his heels, Pierrick was denied at close range by Trueman as he advanced into the area and then the Blues 'keeper was up and on his feet to stop the follow-up by Camarasa.
Ruiz was then replaced, with 19 minutes left, by Kane Thompson-Sommers, therefore moving Bailey back up front. Caolan Boyd-Munce was fielded out to the left, allowing Bellingham to play centrally, in a diamond.
And the change paid immediate dividends, with Bailey scoring the equaliser.
Palace were undone when both Bellingham and Thompson-Sommers harassed them out of possession, midway in the home half.
Thompson-Sommers came out with the ball and laid it on forward for Bailey, to sprint through.
He guided his shot past Stephen Henderson from just inside the area but saw it bounce back off the upright; it popped out straight at him and Bailey did well to remain composed, take a touch, and then lift the ball right-footed high into the net away from defenders desperately trying to recover and protect the goal.
Blues replaced Bailey with Mitchell Roberts with six minutes left and went with three at the back.
It shored them up as well as gave Palace something different to content with at the other end - and Blues so nearly nicked the outcome in their favour.
After forcing a corner, Blues spread panic in the Palace rearguard when Bajrami turned the ball back in from the left of the area and Bellingham caught it on the full, but somehow it stayed out, hitting a defender who was in the way of goal.
In the 90th minute a surge down the right by Gordon fashioned another opening and this time a rasping low Bellingham shot towards the near post was parried and kept at bay by Henderson.
In added-time, Blues swarmed all over Palace as they tried to play from the 'keeper and as Andrews, Thompson-Sommers and Bellingham pressed, the ball came free for Ryan Stirk, and, from the edge of the box, his swerving effort only just cleared the crossbar.
Blues (4-4-2): Trueman, Gordon, Burke, Stirk, Bajrami, Redmond, Concannon (Andrews 63), Boyd-Munce, Bailey (Mitchell Roberts 84), Ruiz (Thompson-Sommers 71), Bellingham. Subs not used: Ramos, Forrest.