The Saints came close to an opener in the sixth minute when Kirk Broadfoot's close-range effort was blocked by Colin Stewart, then John O'Neill blasted the rebound over the crossbar.
The Saints' goal had a real let-off in the 19th minute when a poor clearance from Craig Hinchcliffe fell to Don Cowie 30 yards from goal, but his attempted lob just cleared the crossbar.
County were coming closer and John Rankin got on the end of a Cowie cross, flashing a header wide of Hinchcliffe's left-hand post.
County's best chance of the half fell David Winters, who failed to get his header on target after a diagonal ball from Cowie.
A dreadful blunder by County captain Jim Lauchlan led to the only goal of the game. Kean slipped in behind the defence and fired the ball off the inside of the post and into the net.
Saints almost established their lead and at the start of the second half David van Zanten slipped the ball through to Kean and the striker was not far away with a low drive.
That was Kean's last action in the game as he suffered a bad ankle knock and was replaced by Brian McGinty.
County brought on Steven McGarry to face his old team at the expense of Stewart and the substitute set up Winters with a great through ball, but the chance was again lost.
County tried hard to get back on level terms, but a long-range effort from Rankin was the best they could offer.