Dimitri Payet scored another wonder goal but West Ham were forced to settle for a 2-2 draw with Crystal Palace after being reduced to ten men late in the game when Cheikhou Kouyate was shown a controversial red card.
After Damien Delaney had headed Palace into the lead early in the game, the Hammers hit back straight away when Manuel Lanzini brought the home side level.
Payet then scored another superb free-kick just before half-time and the home side were set for another three points as they look to keep their Champions League hopes alive.
But the major turning point came on 67 minutes when Kouyate was shown a straight red card for a challenge on substitute Dwight Gayle, much to the anger of the Slaven Bilic and the West Ham supporters.
Palace made the extra man count as Gayle converted from close-range following a mistake by Angelo Ogbonna.
The result keeps the Hammers in fifth position but the European dream is still very much alive as the Club prepare for two big games against Arsenal next Saturday and then Manchester United in the FA Cup quarter final replay.
Palace opened the scoring on 15 minutes after Bakary Sako's curling free-kick was palmed away by Adrian but straight into the path of Delaney who headed the ball into the corner from the tightest of angles.
But the home side hit back straight away and grabbed an equaliser on 18 minutes when Michail Antonio's cross from the right fell to Diafra Sakho who headed the ball back into the path of Lanzini and he made it two goals in two games with another clinical finish into the bottom corner.
The goal ignited the home side and they could have doubled their lead when Sakho's first time shot was well saved by Palace keeper Wayne Hennessey on 21 minutes.
Payet also came close on 23 minutes when he weaved his way to the edge of the box before striking a low shot which produced a fine save from Hennessey.
The home side could have been made to pay for those missed opportunities when Sako played in a superb cross from the left hand side on 33 minutes that picked out Jason Puncheon who volleyed the ball inches wide of the goal.
In an open contest the Hammers had another great chance on 39 minutes when Payet's corner to the far post picked out Sakho who rose the highest inside the box but he directed his header just past the post.
But the best moment of the game came on 40 minutes when that man Payet got on the scoresheet once again after he was brought down on the edge of the box.
After curling a previous effort just over the bar the crowd anticipated something special was about to happen and they were proved right once again.
After scoring another spectacular set-piece for France during the week, the French magician followed that up with another outstanding effort.
Despite Palace having seven men in the wall, Payet showed his quality by striking the ball into the opposite corner and the ball flew in off the bar and post.
It was another unstoppable effort from the Hammers superstar who took his tally to 12 goals this season.
The Hammers looked to make it three and Lanzini came close on 56 minutes when he broke free into the Palace half and fired a shot which Hennessey saved diving down to his right hand side.
The home side were let off the hook on 65 minutes after Kouyate played a poor backpass which forced Adrian to race out of his goal and clear the ball away.
The rebound fell to Sako who saw his shot superbly cleared off the line by Aaron Cresswell.
The turning point in the game then followed on 67 minutes when Kouyate was shown a straight red card for a challenge on Gayle.
Palace were determined to make the extra man pay and could have drawn level on 72 minutes when Yannick Bolasie's cross from the right hand side picked out Sako who fired a volley wide of the post.
The south London side made it 2-2 on 75 minutes when Ogbonna failed to deal with a cross from Pape Souare and the ball fell perfectly for substitute Gayle who slotted the ball past Adrian into the corner of the net.
The Hammers were forced to settle for a point but maintained their superb home record and are still only three points behind Manchester City as the club look to keep alive their hopes of securing a top four finish.
West Ham: Adrian, Antonio, Reid, Ogbonna, Cresswell, Kouyate, Noble (Obiang 80), Emenike (Carroll 60), Lanzini, Payet, Sakho (Valencia 68)
Subs not used: Randolph, Song, Tomkins, Moses
Bookings: Noble, Reid
Red Card: Kouyate
Crystal Palace: Hennessey, Ward, Dann, Delaney, Souare, Jedinak, Ledley (Campbell 70), Zaha (Gayle 46), Bolasie, Puncheon, Sako
Subs not used: Mariappa, McCarthy, Lee, Mutch, Kelly
Bookings: Ward, Sako
Referee: Mark Clattenburg (Tyne & Wear)
Attendance: 34,857