Target man Iwelumo, who was playing his football in Germany last season, came up trumps with the only goal of the game in the 48th minute.
Karl Duguid provided an inch-perfect cross from the right edge of the penalty area for Iwelumo to send a downward header into the bottom corner of the net, giving keeper Nick Colgan no chance at all.
Colchester had lost their first two games of the campaign at Gillingham and against Swansea, but they never looked like relinquishing their lead against a below-par Barnsley side.
The Yorkshire visitors rarely looked like grabbing an equaliser and it was Colgan who was required to prevent Colchester from adding to their tally as the game wore on.
The busy Colgan saved well from a long-range shot by Greg Halford who was operating up front with Iwelumo for the first time this season.
Colgan denied Neil Danns his second goal of the campaign in the 75th minute. Danns met Iewlumo's knockdown with an overhead kick that was superbly palmed away by the agile goalkeeper.
In the 82nd minute, Danns capped a strong run with a 25-yard effort that Colgan managed to hold on to, and Barnsley's keeper then made the save of the afternoon with just four minutes remaining.
Substitute Gareth Williams looped over a cross which Iwelumo connected with a scissor kick. It looked a goal all the way only for Colgan to somehow half-volley the ball over his own bar while lying on the deck.
Barnsley's best chances had arrived around the hour mark. Summer signing Paul Hayes was just a foot wide with a curling 20-yard shot and shortly afterwards his strike-partner, Daniel Nardiello, was agonisingly close with a header from Neil Austin's cross that dropped just the wrong side of the post.