The Scotland international, who was a summer signing from Wolves, headed home on the stroke of half-time to ensure a winning start for Brian Laws' men.
Forest, who were beaten play-off semi-finalists last term, had opportunities to level with Nathan Tyson guilty of wasting their best opportunity, while Robert Earnshaw hit the post.
It was just the start that Laws will have been looking for after last season's relegation and he will be hoping that it kick-starts a promotion push.
Billy Davies will be keen for his side not to repeat their disappointing away form that dogged the latter part of last season, where they did not win any of their final 11 fixtures on the road.
Laws handed debuts to Ross Wallace, Iwelumo and Dean Marney, though goalkeeper Lee Grant had to be content with a place on the bench.
Forest named loan signing Ryan Bertrand in their starting line-up and they made the better start as they knocked the ball around confidently.
Striker Earnshaw had already gone close with a long-distance effort before he went even closer to giving his side the lead in the 23rd minute.
The 29-year-old picked up a loose ball on the edge of the area and created space for himself before unleashing a low shot which beat Brian Jensen, but rebounded back off the upright.
Forest were on top and they wasted another opportunity when Tyson broke clear, but with two team-mates well placed in the centre, the striker over-hit his pass.
The hosts finally stirred as the first half wore on and created a couple of decent chances.
Wallace whipped in a dangerous across which just evaded Iwelumo and Andre Bikey had a header hacked away by Forest's Chris Cohen.
And the momentum which Burnley had built paid dividends on the stroke of the interval as they took the lead with a fine goal.
The dangerous Wade Elliott advanced down the right and after a neat interchange with Martin Paterson he delivered an inviting cross for Iwelumo, who finished in emphatic style with a diving header.
Laws' men began the second half as they had ended the first and could have doubled their lead but Clarke Carlisle's header was kept out by Lee Camp.
Forest searched for a way back into the game and Tyson was guilty of wasting a glorious chance to level.
Earnshaw did well to create space and slip his strike partner in, but with the goal at his mercy, Tyson could only fire high and wide.
The game became an end-to-end affair and Burnley continued to look dangerous, with Marney heading over Wallace's cross.
Davies' men continued to push, though, and Dexter Blackstock should have done better when he headed Chris Gunter's cross over the bar.
But it was Burnley that created the better chances in the latter stages with Iwelumo and Marney again going close, but Iwelumo's first-half strike proved the decisive moment.
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