Josh King's equaliser two minutes from time cancelled out the Ivorian's sensational solo goal, and comes after Palace dropped points thanks to late goals in recent defeats to Tottenham Hotspur, Manchester United and Liverpool.
Luka Milivojevic had given the south Londoners the lead with an excellent free-kick following a goalless first half, but substitute Lys Mousset made it 1-1.
Bournemouth edge incident-free first half
The Cherries could have led on no fewer than three occasions inside the opening five minutes. Callum Wilson and Dan Gosling both somehow missed the target with the net seemingly set to ripple, and when they did finally shoot at Wayne Hennessey's goal, the Wales international did well to deny Jermain Defoe.
Defoe had four goals in his last two appearances against Palace prior to this game, having scored a brace in December's reverse fixture and scoring twice in Sunderland's 4-0 rout at Selhurst Park last season, but was denied a fifth in three by a fantastic tackle from Aaron Wan-Bissaka when the England forward seemed destined to tap home from close range.
Palace eventually improved following the early assault on their goal, and could have led had it not been for a good block by Nathan Ake to deny James McArthur.
But it was in the second half that the game finally burst into life. Palace were awarded a free-kick 25 yards from goal just minutes into the second period, and Luka Milivojevic stepped up to curl home to score his tenth goal of the season.
Patrick van Aanholt had an excellent opportunity to double Palace's advantage but was denied by Asmir Begovic when put one-on-one with the Bosnian by Zaha.
And it proved costly when the hosts were level moments later. Mousset had only been on the pitch for two minutes when he curled beyond Hennessey when he was teed up outside the box by Ryan Fraser.
Zaha had been frustrating, skying one particular effort over the bar while seemingly bowing to the jeers from the home crowd, and still seemed to be carrying the injury that has seen him miss a large portion of the last two months. But when he received the ball on the edge of the box from Andros Townsend, pirouetted around Fraser's sliding tackle, leaving the Scot sprawling across the turf, and slammed home left-footed via a slight deflection off Steve Cook, it was a moment of unmitigated artistry that will be one reason why a big club could be tempted into spending upwards of £40 million for a player who Palace are so reliant on.
It seemed to have won the game for Palace, just their second success in nine points, but it was another Palace academy graduate who cost them the points at the other end in the final few minutes. 20-year-old Wan-Bissaka has been almost faultless since his debut against Tottenham in February, but it was he who lost track of King at a corner and the Norway international tapped home Cook's flick-on to snatch a point for Eddie Howe's side.