Bob McHugh cashed in eight minutes from time after a horrific defensive blunder by Coll Donaldson to complete a double and give Morton all three points.
Morton had failed to beat Inverness in their last seven clashes and, to add to that, David Hopkins’ side had chalked up just one win in their last seven outings. But they wasted no time in trying to improve on that dismal record by taking the lead after just six minutes.
Peter Grant put McHugh through to beat the offside trap and brilliantly lob goalkeeper Mark Ridgers from 15 yards.
Caley Thistle came to Cappielow with just one defeat in their last ten matches in all competitions and almost levelled after 13 minutes but Carl Tremarco’s close-range header came back off a post.
Two minutes later Miles Storey found James Keatings racing in from the right but goalkeeper Sam Ramsbottom got down well to block.
Inverness had another opportunity after 24 minutes when a Keatings free-kick from the left was only partially cleared, but Storey blasted over from 16 yards.
The equaliser finally came in 27 minutes when Keatings was again the provider when he headed the ball into the path of Mitchell Curry, who rifled a right-foot angled drive low into the far corner of the net. But McHugh had the last word.