Platt's close-range header and Jutkiewicz's penalty put the Sky Blues two goals to the good and though Jason Scotland grabbed one back, it proved to be a mere consolation.
Coventry had not won at Ipswich since April 1994, however, their margin of victory could have been wider but further efforts from Jutkiewicz and Platt struck the bar and post respectively.
Ipswich made just one change from the team that beat Leeds two weeks ago as Luke Hyam returned from suspension to replace Tom Eastman, who dropped to the bench.
Coventry boss Aidy Boothroyd also made just a single change from the goalless draw at Hull as Gary McSheffrey came in for Daniel Ward.
The game began rather slowly, though Sky Blues striker Jutkiewicz shot narrowly over from inside the area.
As well as their record at Ipswich, Coventry's recent record on their travels was just as poor as they had won just once in 10 games on the road, so it was a surprise when they took the lead after 19 minutes.
Sammy Clingan's left-wing corner found Aron Gunnarsson at the far post and he nodded the ball back across the area to Platt, who powered his header past Town goalkeeper Marton Fulop.
Buoyed by their opener, the visitors attacked with venom, however, it was Ipswich midfielder Jake Livermore who nearly levelled matters with a 25-yard strike that went fractionally wide of the post.
The strike duo of Platt and Jutkiewicz were running riot against the Ipswich defence and their combination almost saw Coventry double their lead.
Platt put Jutkiewicz clear, however, the 21-year-old's fierce shot from 12 yards came back off the underside of the crossbar.
It was certainly a let-off for Ipswich, who were second best throughout the opening 45 minutes though Gareth McAuley headed wide from six yards, which denied the hosts a scarcely-deserved equaliser.
Tractor Boys manager Roy Keane shuffled his formation and brought on Connor Wickham after the interval.
It initially seemed to work as Ipswich laid siege to the Coventry goal in the opening minutes of the second-half, with Jason Scotland's point-blank strike forcing a fine save from Keiren Westwood on his 250th career appearance.
However, Town were caught on the break and Jutkiewicz was brought down by a clumsy challenge from McAuley to give City a penalty.
Jutkiewicz opted to take the 56th-minute spot kick himself and he made no mistake by sending Fulop the wrong way.
Almost immediately though, Jason Scotland halved the deficit when his first-time strike from Jaime Peters' right-wing cross found the back of the net.
It was a lifeline for Ipswich but Gunnarsson should have regained the two-goal cushion for the visitors when his close-range header sailed wide of the target.
Although Keane's men were doing the pressing, they were again bailed out by the woodwork as Platt's glancing header from Clingan's free-kick struck the post.
For the last quarter of an hour, Ipswich dominated the clash though the closest they came to finding a leveller was Scotland's strike from 12 yards, which was magnificently tipped round the post by Westwood.