Wright powered home a header from fellow full-back Liam Rosenior's cross on 66 minutes and this time they managed to hang on after several games in which they have lost a late lead.
Injury-stricken Derby came for a 0-0 draw, with Paul Dickov their only fit forward and forced to play as a lone striker who lacked support for the most part, as the visitors were happy to stifle Ipswich.
The plan worked in a dour first half in which neither side looked remotely like scoring, and showed exactly why they have spent the season in the lower reaches of the Championship table.
Dickov did have a decent early chance from Gary Teale's deep cross, but he sent his right foot volley into the side-netting from an acute angle.
Ipswich took their time to settle, but then produced a few minutes of pressure as first the recalled Jon Stead shot wide before Alan Quinn tumbled in the box under Bryan Hughes' challenge, but referee Anthony Taylor rejected what looked a good penalty shout.
Liam Trotter had two shots charged down after Derby failed to clear a Grant Leadbitter free-kick, but the game then went through a lengthy spell in which neither team threatened.
The game finally perked up as half-time approached, with Stephen Bywater saving headers from central defenders Damien Delaney and Alex Bruce, while Teale fired one effort wide and then set up Robbie Savage for a fierce drive which Asmir Begovic saved.
The best chance fell to Savage in a quick breakaway which he instigated and he should have finished it off with a goal, only to slip after Teale's cross found him in space in front of goal.
Bywater saved again from a Bruce header as Ipswich looked to start the second half on the front foot, but it was Derby who came close next as Begovic made a fine reflex save to deny Dickov, although the forward was ruled offside, and the Portsmouth loanee then palmed over a stinging Teale drive.
Begovic superbly tipped away a cross-cum-shot by Hughes before Keane sent on subs Tamas Priskin and Pablo Counago in place of the ineffective Stead and Trotter, and it perked up the hosts.
Quinn had a 30-yarder gathered by the diving Bywater, Carlos Edwards fired wide from 35 yards, before Town got the breakthrough as Rosenior's perfect hanging cross was thundered home by the head of Wright, and although Bywater got a touch he couldn't keep it out.
Priskin curled an effort wide as Town went in search of a quick second, before Derby had a great chance when Savage's clever chipped pass found Hughes behind the home defence, but Begovic turned aside his firm drive.
A poor clearance by Jonathan Walters back to help his defenders saw Frederik Stoor charge it down and Dickov volley over, while Counago and Walters shot wide and then Priskin wasted a one-on-one with Bywater, sending his shot too near the visiting 'keeper, who gathered at the second attempt.
Home fans had to endure four added minutes and in the final one a bit of penalty area pin-ball finally saw the ball drop to Hughes who volleyed over.
The whistle sounded moments later much to the relief of the majority inside Portman Road.