Alexis Sanchez headed in Danny Welbeck`s chip to give the Gunners the lead but they lacked a killer instinct to put the result beyond doubt.
Bolasie then struck from distance, beating Petr Cech at his near post.
The Congolese forward`s equaliser alarmingly sucked the energy out of Arsenal and it was their London rivals who seemed more likely to score in the dying minutes.
Wilfried Zaha had the home defence backpedalling with a surging run into the box, but luckily for the Gunners a heavy touch from the winger allowed Gabriel to nick the ball.
It was a performance which summed up Arsenal`s season. They missed a number of opportunities, had more than 70% of the possession but once again failed to secure three points in a match they were expected to win.
Arsenal home form worrying
The Gunners have collected eight points from their past six home games and it is that form which has ruined their title hopes and is threatening to wreck their ambitions of competing in next season`s Champions League.
Arsenal still enjoy a four-point cushion over Manchester United in fifth and are level on points with City in third, but two draws in their past two games has increased the pressure on Arsene Wenger and his men in the run-in.
Wenger has not failed to qualify for the Champions League during his 20-year tenure, but his critics will point out that neither has the club finished higher than third in their past 10 campaigns.
The tale of this match was a familiar one to Arsenal fans and a nervous energy remained around the stadium even after Sanchez had put the hosts ahead in first-half stoppage time.
Arsenal created chances, notably Ozil and Sanchez free-kicks, a hooked Danny Welbeck effort and another Sanchez header. Midway through the second half nine Arsenal players had made more passes than Palace`s top passer, but as has often been the case, the Gunners were unable to put the game to bed.
No flair, but Palace won`t care
Palace enjoyed their first victory of the year last weekend, courtesy of Jason Puncheon`s winner over Norwich, but they remain winless on the road in eight league matches.
There was no hint in the first half that the FA Cup semi-finalists would snatch a point from this match. Rarely did they visit the opposition half and all their energy went into containing the creativity of Ozil and Sanchez.
But manager Alan Pardew must be praised for his attacking substitutions after the break, introducing former Arsenal striker Emmanuel Adebayor, much to the chagrin of the home support, and Zaha to support the lively Bolasie.
Even with extra creativity in their ranks, the visitors created little. Until Bakary Sako`s header from a corner in the 76th minute they had had no chance on goal in the second half.
But with a point giving the Londoners an extra cushion from the relegation scrap between Newcastle, Sunderland and Norwich, Pardew will care little about his team`s lack of flair at Emirates Stadium.
What the managers said
Arsenal boss Arsene Wenger:"It is very difficult - we had a lot of possession but did not make enough of it. We lacked a change of pace, sharpness.
"They defended well. We put a lot of effort in but came out with a frustrating result. It is hard to accept but the competition goes on and we focus on the next one.
"I don`t know how it works mathematically but we are too disappointed to think about the league. We have to think about the Champions League and fight to be in the Champions League.
"We have another home game on Thursday and have to prepare for that."
Crystal Palace boss Alan Pardew: "It was an important point for us. It means two of the teams below us have to get 40 points and with our goal difference it will be difficult for them.
"It makes it easier for us to look forward to the FA Cup semi-final and look to get to mid table which is where I think we belong.
What next?
Crystal Palace travel to Old Trafford on Wednesday to play Manchester United before turning their attention to an FA Cup semi-final on 24 April against Watford. Arsenal will next host West Brom on 21 April before matches with relegation-threatened Sunderland and Norwich.
