All of the goalmouth action occurred in an incredible first half at St Mary's Stadium on Saturday, as Chamakh struck either side of Yaya Sanogo's first goal for Palace to ensure progress.
Graziano Pelle gave Southampton an early lead from a corner, but that advantage was short-lived as Chamakh levelled by converting a rebound.
Scott Dann's own goal restored the home side's lead, but once again Palace's response was swift when Sanogo shot home to make it 2-2 after just 21 minutes.
The result means Palace have now won all four matches under the leadership of Alan Pardew, while defeat for one of his former clubs ended an eight-match unbeaten run in all competitions.
Palace failed to deal with James Ward-Prowse's corner, and Pelle was on hand to bundle home his first goal in eight games.
The visitors were level within two minutes, however, as Chamakh poked home after Fraser Forster had spilled Sanogo's shot.
Forster kept out Sanogo soon afterwards, and Southampton were grateful for that save as they restored their advantage in the 16th minute when Ryan Bertrand's cross was turned into his own net by Dann after a breakdown in communication with goalkeeper Wayne Hennessey.
Forster then denied Fraizer Campbell as the all-action opening continued, but three minutes later the keeper was unable to prevent Sanogo from equalising for a second time as the striker converted from Zaha's pass.
In the second half, Ronald Koeman introduced Shane Long off the bench in a bid to find an equaliser, but the forward's contribution lasted just 13 minutes as he left the field having hurt his right arm in a collision with Ward.
Southampton pressed hard in the final stages to earn themselves a replay and Hennessey produced a fine save to keep out Eljero Elia's drive two minutes from time, which allowed Palace to hold firm and book their place in the fifth round for the first time since 2010.
