Kerr succeeded Ian McCall in midweek but he was unable to get the winning start he craved as Dundee took a two-goal lead through Declan McDaid and Paul McGowan before Luke McCowan reduced the leeway.
McDaid, who spent two and a half seasons at Ayr before heading to Dens Park in the summer, silenced the home supporters in the 16th minute when he drove into the bottom corner from 20 yards after Andrew Nelson supplied him.
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Hide AdDundee increased their advantage when McGowan cashed in to drive home after Ross Doohan had saved from Jordan Forster following a Graham Dorrans free-kick.
The double hammer blow was sore on Ayr who had played with plenty of invention but they struck back seven minutes before the interval.
Aaron Muirhead got his head to a Stephen Kelly cross and teenager McCowan was at the back post to head his seventh goal of the campaign.
Three minutes into the second period they introduced another striker in Craig Moore who was making his first appearance of the season after a long battle against injury.
The Dundee defence came under heavy pressure, only relieved by some lightning quick breaks from the speedy McDaid, and they held on to occupy fourth place, only three points behind the leaders
