John Robertson’s team fell ten points adrift of the play-off zone on a day when fortune deserted them and the Cappielow side cannily exploited chinks in the armour.
The hosts had two goals chalked off, cracked the woodwork twice and had a penalty claim waved away, but Jim Duffy’s men were otherwise strong and resolute.
Scott Tiffoney made the difference, netting the first-half opener and winning a second-half penalty for Gary Harkins to tuck away as Morton made it six wins from the last seven.
Duffy, while thrilled by the club’s first ever win in the Highlands, stressed: “The table is good to look at but this division is so precarious you can’t take your eye off the ball for a second.”
The opener came on 28 minutes. A long punt forward from goalkeeper Derek Gaston was mis-judged by Brad McKay and Tiffoney raced through to net at the second attempt after McKay made an initial recovering block.
Collin Seedorf clipped Tiffoney on 71 minutes and Harkins struck the spot-kick in off the left-hand post.
“It’s going to be tough to reach the play-offs now but there is 12 matches left,” said Inverness boss Robertson.