And the season-long loan for influential midfielder Alexei Eremenko could end this month if Metalist Kharkiv decide to sell the playmaker.
But Esson was busy again on the hour when Eremenko danced through the home defence to set up a shooting opportunity.
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 Alexei Eremenko, whose impressive form on loan to Kilmarnock from Metalist Kharkiv has attracted the interest of other clubs.
Moments later, Inverness goalkeeper Esson produced an acrobatic diving save to push wide a 30-yard free-kick from Eremenko, with Bryson volleying just wide soon after.
Frazer Wright then squandered a great chance to double the lead when he was unchallenged to power a header just wide from an Eremenko corner.
Eremenko was fouled in the box by keeper Jamie Langfield and Jamie Hamill stroked home the resulting penalty, then Sammon came close again before the end.
Alexei Eremenko 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.
But Paatelainen said Aubameyang was not being viewed as a potential replacement for Eremenko should Metalist accept an offer for the Finland international before the January transfer window closes.
After a sluggish start, Kilmarnock found their passing rhythm, with Mehdi Taouil and Alexei Eremenko pulling the strings in midfield, and Inverness were picked off on the counter-attack time-after-time.
Midfield schemer Alexei Eremenko 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 Alexei Eremenko 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.
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