After the visitors had the best of the opening half, Coventry scored at either end of the second period - Elliott Ward firing home a spot kick after 47 minutes and Leon McKenzie finishing off from close range after coming on as a substitute.
Chances were few and far between in a tense first half in which Norwich City offered the biggest attacking threat.
Both managers had given six players their debuts and some settled quicker than others as both teams looked to get off to the best possible start to the season.
Arturo Lupoli had several sights of goal early on but on several occasions he was denied by the impeccable Ward, who made two or three key blocks.
Sammy Clingan fired a long-range shot wide as Norwich edged the territorial advantage over the home team.
Coventry's new strike partnership of Freddy Eastwood and Clinton Morrison struggled to get on the ball in the first half as the home team failed to muster an effort on target.
Norwich defender Dejan Stefanovic was lucky to avoid a red card on his debut for the Canaries as he caught Jay Tabb's ankles on the edge of the area, but referee Colin Webster only booked the centre-back.
Coventry took the lead at the start of the second half from the penalty spot.
Guillaume Beuzelin was brought down by Clingan on the right-hand side of the box and Ward made no mistake with penalty on 47 minutes.
The visitors had plenty of chances to draw level. Lee Croft lost his footing at the key moment after 50 minutes when he could have crossed to the back post.
Lupoli headed over seconds later when the goal was gaping and his replacement Omar Koroma was denied an equaliser by an outstanding save from Keiren Westwood after 69 minutes.
Norwich had a great case for a penalty of their own when Dan Fox dragged down Wes Hoolahan in the box but, as the referee waved away their claims, Croft struck a fierce shot which produced another outstanding save from Westwood.
Despite the visitors' best efforts, Coventry doubled their lead at the death as Morrison's deft chip came back off the bar and McKenzie was on hand to tap in.