Kelly opened the scoring from the penalty spot after Dons goalkeeper Jamie Langfield had been sent off for bringing down Borja Perez, and the midfielder struck from the edge of the area to double his side's lead in the dying stages.
Aberdeen have not had their troubles to seek in recent weeks and their lengthy injury list showed no signs of abating with captain Russell Anderson and midfielder Stephen Hughes, rated the two most likely to return for this match, both missing out.
As a result, Craig Brown stuck by the same XI who had started the midweek Scottish Cup win over Motherwell.
Kilmarnock made two changes from the side that had lost 3-1 to Celtic a week ago, with Mo Sissoko and captain Manuel Pascali returning to the side in place of Ryan O'Leary and Danny Racchi respectively.
It was the visitors who were first to threaten in the opening stages, with Gary Harkins playing a delightful flick to Perez, but the Spaniard sent his effort wide of the post.
Midway through the first half, Paul Heffernan sniffed out an opportunity for Killie as he seized upon a loose ball from a corner, but Andy Considine blocked his eight-yard strike.
At the other end, from a Johnny Hayes cross, midweek goalscorer Joe Shaughnessy came close to a second in as many games when his back-post header narrowly over the crossbar.
Killie were presented with a free-kick 20 yards out with 10 minutes of the first half remaining, but former Celtic man Cillian Sheridan could not take advantage, sending his left-footed effort curling over the crossbar.
But they took the lead from the penalty spot on the stroke of half-time.
Perez ghosted his way into the area before going down under the challenge of Langfield, and Craig Charleston had no hesitation in pointing to the spot.
Langfield was shown a red card for his misdemeanour and, with Rory Fallon sacrificed for substitute goalkeeper Jason Brown, Kelly stepped up to blast home from 12 yards.
And they could have had a second soon after the restart. Kelly had acres of space to cross from the left and found Heffernan, but the striker headed wide of the post.
Kilmarnock replaced Sissoko shortly after, former Don Ryan O'Leary replacing him in the heart of defence with the Killie man having picked up a booking late in the first half. Just minutes later, Jamie Fowler collected the game's second yellow card.
The Dons had the ball in the net after 58 minutes, Josh Magennis having won an aerial challenge with Cameron Bell and bundled the ball over the line, but he was penalised for his challenge on the goalkeeper, and the goal was disallowed.
Despite their numerical disadvantage, Aberdeen were having a right good go at their opponents, but Hayes picked up a booking for dissent when his frustration boiled over when they were denied what seemed a clear corner.
With 67 minutes gone they were just inches away from the leveller, Magennis crashing a shot off the crossbar from 30 yards, with Bell left stranded well off his line.
And the keeper was at full stretch to turn a Niall McGinn free-kick round the post two minutes later, after Pascali had brought Hayes down just outside the area.
But the game was won for the visitors with four minutes left.
A neat move down the left flank saw substitute Rory McKenzie, amid furious claims for off-side, cut the ball back to Kelly on the edge of the area, and the midfielder sent a low shot inside Brown's right-hand post.
Mark Reynolds was the final player to enter the referee's notebook for a late foul in injury time.
- Sports & Recreation
- Jamie Langfield