Ipswich played some excellent attacking football and repeatedly exposed the Coventry defence but they could not quite find the equaliser that their second-half play in particular deserved.
The visiting team looked as though they were going to blow away an uncertain Coventry during the opening minutes of the contest and it took some desperate defending to block a shot from Peters before Gareth McAuley headed wide from a corner.
But Coventry opened the scoring in spectacular style after a ponderous Ipswich backline failed to deal with a lengthy goal-kick after 10 minutes.
Richard Wright had raced out of goal but failed to collect the ball and Morrison controlled it in a wide area towards the edge of the Ipswich area. The Sky Blues striker still had a lot to do but after taking two touches to position himself, he finished with a great deal of skill and composure.
His second was more instinctive as he met a whipped-in cross from Isaac Osbourne with a crisp header after more hesitant defending from the away team.
Morrison's brace helped Coventry build a 2-0 lead before Ipswich countered
Ipswich might have had a penalty between the two Coventry goals after Ben Turner appeared to bring down Lee Martin but their appeals fell on deaf ears.
But they did reduce the deficit through a composed finish from Walters after Martin's through ball had completely exposed a Coventry defence that was woefully out of position.
Keane's side played some attractive counter attacking football before the break but Martin twice failed to conjure the quality of finish that that such well-constructed approach work deserved.
Canada international Peters was a lively attacking presence for the Tractor Boys until he was withdrawn after 66 minutes and the 22-year-old was unfortunate to see a crisp 20-yard strike drift inches wide after taking a slight deflection shortly after the restart.
He then profited from a clever lay-off from Jon Stead but his six-yard strike was saved by Westwood.
Ipswich lost David Norris to injury but it did not detract from the visitors' increasing superiority and Keane later outlined his ambition with the introduction of Tamas Priskin and 16-year-old Connor Wickham.
An unmarked Balkestein wastefully headed wide from a corner before goalscorer Walters narrowly missed the target with an ambitious long-range strike across goal.
A brilliant looping header from Walters almost breached Westwood's defences but the goalkeeper made a sensational fingertip save, while another Balkestein header finally beat the Coventry stopper but was nodded clear by Morrison.
Coventry worked hard to shut down their opponents and showed excellent determination to resist an increasingly rampant Ipswich, but there was a hint of fortune as Westwood saved a Martin strike with his legs close to the final whistle.
Coventry boss Chris Coleman: "All the talk before the game was about Ipswich and Roy Keane and where they'll finish but I prefer that.
"We won't come up against a stronger side and we were flustered at set-plays but we got through it and no one went missing in my side.
"I'm sure Roy will go back home and kick his cat because he hates losing but that's a feather in our cap."
Ipswich boss Roy Keane: "We gave two very poor goals away and lacked sharpness in the final third but that will come in the coming weeks and months.
"The first goal came from a goal-kick and the starting position of everyone was very poor.
"And the second one, Clinton has headed it at knee height. If you're a defender and he heads it that low you take his head off, it's as simple as that.
"I'll be down tonight but the day my appetite isn't affected by defeat I'll be out of the game. I am trying to learn from my experiences at Sunderland and not get too downhearted but I will not get home, put my feet up and have a whistle.
"But I've been like that since I was eight or nine years old. the beauty of it is that we have a game on Tuesday night so that can cheer me up.
"There will always be disappointments in football but I will be okay - don't worry about me.
"This will put a dampener on my birthday for sure but Roy Keane's birthday is not, and should not be, important in the grand scheme of things."
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