Morrison sprung a nervous Southampton offside trap 15 minutes from time before calmly placing his finish past the out-stretched arm of goalkeeper Kelvin Davis.
Saints had taken the lead just seven minutes earlier as David McGoldrick controlled a Lloyd James cross to pick his spot at the far post with precision.
Coventry's one-dimensional style was difficult to watch and as Southampton passed their way across the park with ease a home win looked inevitable.
Midfielders Andrew Surman and Adam Lallana combined on five minutes for the England Under-21 midfielder to unfortunately place his shot straight at Keiren Westwood.
A menacing Rudi Skacel cross was heading straight for Jason Euell only for the ball to ricochet off the back of Elliott Ward and force Westwood into a diving save.
For all their possession though Saints lacked the necessary penetration to genuinely pose a scoring threat and Skacel then nearly undid all their hard work as his misplaced back-header fell at the feet of the opportunistic Morrison on 34 minutes.
The Coventry striker chipped an on-rushing Davis but as the ball drifted towards goal captain Paul Wotton was on hand to clear their lines.
Five minutes before the break Euell broke free on the right and despite initially stumbling kept his feet to deliver a pin-point cross to McGoldrick in space.
The young forward connected perfectly, but sent his powerful volley straight at Westwood where either side would have resulted in a certain goal.
Coventry's tiresome long-ball tactics finally bore some results of sort as an Aron Gunnarsson long throw was poorly dealt with and Freddy Eastwood's half-volley was palmed away by Davis.
The second half opened up marginally more than the first and McGoldrick atoned for his earlier miss as James' dipping cross was well tamed before he steadied himself to nestle a right-foot finish into the far corner.
Having just one home league win to their name all season, the Saints then retreated, allowing Coventry the ball and the impetus to seek an equaliser and when Guillaume Beuzelin's through ball found Morrison, there was only one outcome.