Haynes slotted home in the 40th minute to complete a fine comeback by the hosts after Norwich had taken a shock fourth minute lead.
Town dominated though, and only a fine performance from David Marshall in goal and some poor Ipswich finishing kept the scoreline so close.
The visitors had got of to the best possible start when Ched Evans seized on a loose ball to fire a low 25-yard drive beyond Stephen Bywater.
Ipswich were level on 13 minutes when the outstanding Pablo Counago played in Haynes and his low drive went in off the shins of City's Alex Pearce.
David Marshall made a good diving save from Tommy Miller's free-kick, and then blocked well to deny Shefki Kuqi after an other sublime Counago throughball.
Marshall also did well to parry an Alex Bruce header from Alan Quinn's corner, with Haynes' follow-up being deflected over.
Marshall beat substitute Jon Walters to a throughball but Counago collected it and slid in Haynes who coolly slotted his fourth senior derby goal beyond Marshall.
Counago nodded Haynes' cross over the bar to end the first half, but if City fans were hoping for a second-half comeback they were sorely mistaken.
Again it was the hosts that dominated, with Miller firing narrowly wide before Haynes shot wide from just six yards after another perfect Counago pass.
Counago and Haynes both missed further chances before a Walters shot shaved the foot of the post with Counago again the creator.
Marshall made his best save on 80 minutes after Miller and Counago had played a neat one-two to put the Spaniard clear, but Marshall saved brilliantly with his feet.
The home fans were getting edgy after watching their side miss so many chances to kill the game, but Norwich failed to create a single worthwhile chance in the second half, despite throwing more and more men forward.
The result puts Town on the fringe of the play-off pack again, while Norwich are still not entirely safe from the drop.