The victory for Wolves was their first away win under new manager Stale Solbakken.
But it was far from funny for Ipswich boss Paul Jewell. The pressure mounted on his shoulders as his Tractor Boys remained second from bottom of the npower Championship with the worst goalscoring record in the division.
Smith's own goal arrived in the 66th minute when he inadvertently turned in Bakary Sako's free-kick from the edge of the six-yard box.
And substitute Doumbia doubled the Molineux men's advantage after 77 minutes when he drilled a delightful right-footed shot beyond the helpless Scott Loach from 22 yards.
Republic of Ireland international Kevin Doyle had twice knocked on the door for Wolves earlier in the half.
First he had a left-foot shot in the 59th minute pushed behind by a full-stretch Loach, and then went even closer three minutes later when his 18-yard drive struck a post.
After a rather uneventful first half, Ipswich had actually made the better start to the second period but Roger Johnson was a tower of strength at the heart of the Wolves rearguard, making two excellent blocks from Lee Martin and Paul Taylor.
The Tractor Boys were then dealt a blow when the lively Taylor hobbled off injured in the 53rd minute, being replaced by striker Jason Scotland.
Ipswich striker Daryl Murphy missed a good chance seconds later when he got on the end of Aaron Creswell's free-kick but sent his shot wide from the centre of the penalty area.
Solbakken left his top scorer Sylvan Ebanks-Blake on the bench until midway through the second half, as a precaution over the striker's tight hamstring. And the men from Molineux certainly missed his pace and movement in the opening 45 minutes.
The visitors tended to hoist long balls towards the front pair of Bjorn Sigurdarson and Doyle but these were too easily mopped up by the Ipswich defence and the contest began to get bogged down in midfield.
Ipswich forward Michael Chopra attempted to liven the proceedings with a left-footed shot from 20 yards in the 26th minute but big centre-back Johnson got in the way.
Ipswich did manage to finish the half in the ascendancy and Martin's mazy 30-yard dribble was only ended by a decent save from Carl Ikeme in the Wolves goal, and the visiting keeper denied Martin again from close range two minutes later.