The only goal of Monday's Portman Road clash came in first-half injury-time. David McGoldrick's cross from the left was missed by Ipswich keeper Marlon Fulop and the ball went into the net off Delaney, who could not get out of the way in time.
Town finished the game with 10 men as Grant Leadbitter was shown a straight red card for a high challenge on Paul Anderson.
A seventh defeat in the last nine league games means Roy Keane's team continue to plummet towards the drop zone.
Conversely, Forest are only two points outside the top six after just one loss
in the last nine matches.
Both managers made five changes following New Year's Day draws. Keane brought in Delaney, Troy Brown, Mark Kennedy, Jake Livermore and Connor Wickham.
Aaron Ramsey was the most notable inclusion for Forest. The Arsenal teenager made only the second start of his loan spell. Also recalled were Anderson, Joel Lynch, Nathan Tyson and the fit-again McGoldrick.
There was little to get the 19,455 crowd excited early on as both teams were restricted to long-range efforts that troubled neither keeper.
Ipswich should have taken the lead with the first real attempt on goal just before the half-hour mark.
Brown met Leadbitter's cross but Lee Camp stuck out a hand and the ball somehow went over the crossbar. Delaney headed over from the resulting corner.
Guy Moussi then had a great chance to put Forest ahead immediately afterwards. McGoldrick put the French midfielder through on goal but he put his shot straight at Fulop.
However, Billy Davies' side would soon be in front courtesy of Delaney's own goal as Fulop failed to gather McGoldrick's cross.
Chris Cohen almost made it 2-0 at the start of the second half but his shot from 12 yards out went just over the crossbar. McGoldrick then went close with a header.
At the other end, Leadbitter and Wickham threatened but failed to work Camp.
That was not the case when McGoldrick let fly from the edge of the area as Fulop had to tip the shot round a post.
Tyson had a good chance to put the game beyond Ipswich but fluffed his lines.
Leadbitter lost control of the ball deep into injury time and was sent off as he over-stretched and clattered into Anderson.