It took just eight minutes for them to go ahead.
Wes Burns opened up the Sky Blues defence down the right and pulled the ball back for Moore, who fired home a powerful low right-foot shot from 10 yards out.
Coventry remained committed and had chances to level.
Ben Sheaf powered a 20-yard shot only just high and wide, before Kasey Palmer and Wright were both denied at point-blank range, while Ellis Simms ballooned badly over.
Ipswich came close to adding a second just before the break when Burns opened Coventry up again and keeper Brad Collins had to produce a great reaction save, diving low to his right to block Nathan Broadhead's downward header.
After starting the second half sluggishly, Coventry then somehow found a way back into the game following a change of match official when referee James Bell went off, to be replaced by Dean Whitestone.
Almost immediately, on 54 minutes, Wright turned to fire in a low right-foot shot and stun the visiting away corner.
However, within five minutes, Ipswich were back in front when Burgess latched on to a deep Leif Davis free-kick.
Burgess' initial header was blocked but the ball ricocheted back to him and his angled follow-up sneaked in for only his second goal of the season.
Last season’s beaten Championship play-off finalists Coventry, whose form has deserted them at the wrong moment of the season, with one point out of a possible 15, had very little left.
There were still 11 fraught minutes of added time for the nervy away section to get through. But the chants of “We are going up” at the final whistle underlined that a second successive promotion is close.
