Conor Sammon's 14th goal of the season gave Killie a half-time lead, the striker converting a rebound shot after Alexei Eremenko's free-kick was saved.
Uncertainty remains about the future of AlexeiEremenko, whose impressive form on loan to Kilmarnock from Metalist Kharkiv has attracted the interest of other clubs.
AlexeiEremenko restored Killie's lead on his debut for the Ayrshire club with a free kick and St Mirren ended with 10 men following Paul McGowan's dismissal.
After a sluggish start, Kilmarnock found their passing rhythm, with Mehdi Taouil and AlexeiEremenko pulling the strings in midfield, and Inverness were picked off on the counter-attack time-after-time.
Midfield schemer AlexeiEremenko returned from a ban but failed to sparkle in the wretched conditions, while former AC Milan man Willy Aubameyang had a quite debut for the Ayrshire team.
Kilmarnock finally threatened in the 27th minute as playmaker AlexeiEremenko played in William Gros with a one-two on the right edge of the box but the French youngster's drive across the target was pushed away by Saints keeper Peter Enckleman.