Schmeichel, a spectator for most of a wretched first half at freezing St Mary's, made some fine saves after the break from Stern John, Jason Euell and Bradley Wright-Phillips.
The young keeper, on loan from Manchester City, pulled off a superb star-jump save - reminiscent of legendary dad Peter - to keep out John's far-post header as the Sky Blues ended a run of eight straight away defeats.
"He reminds everyone of his dad, he's got that presence and makes the goal look small," said Coleman.
"He's got lots of confidence - he's still young and he's only going to get better. We're very happy to have him here."