The match did not really come to life until after the break and in the 64th minute, midfielder Kelly had a tap-in from close range after being set up by Jamie Hamill.
The Buddies tried to fight back but Killie skipper Bryson sealed the win in the 79th minute with a deflected shot from the edge of the box.
The visitors might have increased their lead further before the end but will have been happy to cement their fourth place in the SPL.
But it was another afternoon of woe for the struggling Buddies who remain second bottom.
It was the visitors who made the better start and Jamie Hamill should have given them the lead in the fifth minute but his shot was blocked by Buddies midfielder Sean Lynch.
Patrick Cregg picked up a booking in the 10th minute after a foul on Craig Bryson, after Michael Higdon had blazed over the bar in a rare attack from the home side.
Killie had the chance to open the scoring when Marc McAusland fouled Mehdi Taouil 30 yards from goal but Paul Gallacher blocked Alexei Eremenko’s free-kick.
The Paisley keeper was called into action again when he had to save a Bryson free-kick.
At the other end, his Rugby Park counterpart Cameron Bell produced a more than decent save from Darren McGregor’s volley.
Kilmarnock almost snatched the opener just before the break when striker Conor Sammon mis-hit the ball at the second attempt and Gallacher clawed it back, although the ball appeared to be over the line.
Three minutes after the break Kilmarnock should have taken the lead when Sammon raced clear down the right but his cut-back was missed altogether by Taouil.
But Saints battled back and Higdon had two good chances, the second one the best in the 51st minute when he took a Paul McGowan pass 12 yards out only to sky his shot over the bar.
The game had heated up, with both sides going all out for the opener and the game being enjoyed by both sets of supporters.
As the Buddies took a turn to attack again McGowan had a deflected shot from the edge of the box saved by Bell.
St Mirren boss Danny Lennon changed things around when he brought on Kenny McLean and Gareth Wardlaw for McAusland and Craig Dargo but in the 64th minute it was the visitors who took the lead.
Jamie Hamill took a free-kick from Eremenko on the right and his cut-back across the six-yard box was swept into the net from point-blank range by Kelly, to the joy of the Ayrshire fans behind the goal.
St Mirren rallied, forcing Killie back towards their own penalty area, but at the other end a Bryson drive from 25 yards went just wide.
Killie boss Mixu Paatelainen was spoken to by referee Brian Winter as tensions increased further but as the game edged into its final quarter it was the visitors who were looking the more likely to get the next goal.
And in the 79th minute Bryson sealed the points when his drive from the edge of the box appeared to take a deflection before settling behind Gallacher.
Killie might have had a third when Sammon reached the byline before cutting the ball back for Kelly, but this time the ball was driven high over the bar.
Again, in the 87th minute, Killie raced forward positively but a move involving Taouil and Bryson ended with the former trying a flick which missed the target.
The visitors kept the pressure on until the final whistle but could not get the third which perhaps their second-half display deserved.