Rugby Park's new FieldTurf surface - which will host Scotland's rugby international against Tonga in November - did not give Killie any initial advantage as a team featuring four home debutants as well as Jamie Hamill, back after three years at Hearts, failed to recover from Pawlett's breakaway goal.
Killie had the better early chances and Niall McGinn hit the bar but the first half looked destined to finish goalless until Jonny Hayes broke away to set up Pawlett in the dying seconds.
The home side had a decent flurry of half-chances early in the second period but look like they have plenty to do to replace the 22 goals that Kris Boyd scored last season before leaving for Rangers.
And Jack killed off the contest in the 71st minute when he planted home a header following a wonderful cross by McGinn.
Aberdeen had Hayes and Adam Rooney back in their team following their 3-0 home defeat by Dundee United, but they were slow to start and Jamie Langfield saved a couple of early efforts from Rory McKenzie before rescuing Ashton Taylor in the 12th minute.
The goalkeeper produced an excellent double save from Josh Magennis after the new Aberdeen centre-back had stumbled as the pair chased Craig Samson's kick-out.
There was little goalmouth action in the middle period of the half but McGinn hit the top of the bar 25 minutes in after letting fly from the angle of the box.
Tope Obadeyi then headed over for Killie after good wing play from Chris Johnston, although Magennis got in his way slightly.
The goal came from nowhere as Aberdeen broke quickly and exposed the home defence after Kilmarnock lost the ball in the centre circle.
Hayes raced forward and released Pawlett at the perfect moment and the Scotland Under-21 international sent a left-footed shot in off the bar from a tricky angle.
Aberdeen, who moved to a back three after the break, had a couple of let-offs in the opening stages of the second period.
Manuel Pascali sent a free header wide from Craig Slater's free-kick and Taylor took a major risk when he stopped claiming a tug on his shirt as Magennis ran clear following Ross Barbour's ball over the top.
The decision paid off though as referee Crawford Allan blew for a foul, although only after a delay and amid protests from the home players.
Obadeyi shot not far over from a tight angle and Langfield held McKenzie's ambitious volley as Killie tried to fight back.
But the Dons doubled their lead thanks to McGinn's cross, which gave Jack the simple task of getting his head on the ball and powering it past Samson inside the six-yard box.
Killie threw on Alexei Eremenko and Robbie Muirhead but there was no way back and Dons sub Nicky Low failed to beat Samson from a good chance.
The only down side for the Dons was a late injury for Taylor, who went off with three minutes left after going down despite no apparent challenge.