Scotland striker Iwelumo, on loan from Premier League side Wolves, struck a stunning volley with 17 minutes remaining to settle a dour contest at Selhurst Park.
Iwelumo's spectacular goal from just inside the area was the second of his stay with the club and the Robins' first away goal since Boxing Day.
The result leaves Palace out of the relegation zone on goal difference alone and bursts new manager Paul Hart's bubble after he masterminded a win over Sheffield United in his first game in charge on Saturday.
Buoyed by that win over the Blades at the weekend, Palace started with a spring in their step and had an appeal for a penalty turned down 11 minutes in.
Johannes Ertl's strike appeared to hit the arm of Louis Carey but referee Mike Russell was not interested in any appeals from the home players, deeming that the ball was travelling too fast for any contact to have been intentional.
At the other end City were creating very little, with only weak efforts from Bradley Orr and the recalled Paul Hartley against their name.
City began to grow into the game as it progressed, though, and Iwelumo should have done better with a 12-yard strike after a good run from Liam Fontaine, before ex-Bristol City loanee Calvin Andrew tested Dean Gerken with a deflected low drive for the home side.
Iwelumo and Alan Lee traded efforts that went wide as the start of the second-half failed to better the first for excitement, before Orr worked Julian Speroni with a 20-yard strike.
Then, with the game appearing to be drifting towards a draw, Iwelumo provided the one abiding memory of the contest.
Fontaine's throw-in from the right-hand side found Iwelumo just inside the area and, without a moment's hesitation, he spun and slammed a right-footed volley into the top corner of the goal that left Speroni with no chance.
Jamal Campbell-Ryce looked to add a second for City with a curling effort that Speroni handled well, as the home side, still stunned by Iwelumo's goal, were unable to muster a response.