After losing 1-0 to Norwich City on Saturday, Palace responded in perfect fashion as Chamakh met Barry Bannan's cross to lift his side off the foot of the Premier League table at Sunderland's expense.
West Ham saw a penalty claim waved away in the first half when Kagisho Dikgacoi appeared to handle, while Stewart Downing had a second-half strike ruled out after James Tomkins was penalised for an apparent foul in the build-up.
Palace stole ahead against the run of play on 42 minutes thanks to Chamakh's header, and Cameron Jerome could have made it 2-0 when he went one-on-one with the goalkeeper in the second half.
West Ham pushed for an equaliser and Downing thought he had grabbed one, but his low drive was chalked off due with the linesman’s flag raised.
Carlton Cole was rewarded for his goal in Saturday's 3-0 win over Fulham with a first start since re-signing for West Ham in October, while Palace were unchanged.
The match started at a slow tempo but West Ham soon settled and were on top by the time their penalty appeal was rejected.
Downing's corner appeared to strike the arm of Dikgacoi as Damien Delaney looked to head clear, but referee Lee Mason waved away the protests.
Kevin Nolan wasted a fine chance, volleying tamely at Julian Speroni from eight yards after being picked out by Mark Noble’s scooped free-kick, as West Ham increased the pressure.
Yet it was Palace who moved ahead when Chamakh, unmarked six yards out, glanced home a whipped cross from Bannan after the latter had seen a corner cleared back to him.
West Ham searched for an immediate response and Delaney made a crucial block to deny Downing on the stroke of the interval.
Palace peppered the West Ham goal at the beginning of the second half, with Dikgacoi heading Bannan's centre over the crossbar.
And the home side should have celebrated a second on 53 minutes when Jerome broke free of the West Ham defence only to shoot straight at Jussi Jaaskelainen.
West Ham introduced Joe Cole from the bench and the midfielder looked to have made an instant impact when his deep cross was headed across goal by Tomkins and driven home by Downing.
However, Tomkins was ruled to have been guilty of an infringement.
Palace also had the ball in the net for a second time on 68 minutes through substitute Jimmy Kebe, but Mile Jedinak was offside when he cut the ball back.
The hosts came under the cosh in the closing stages, but held on to secure a second win in three matches and could even have grabbed another goal through Kebe.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1