Steve Jones put Motherwell ahead in the eighth minute when his 20-yard strike caught out Cammy Bell at his near post, but Aubameyang netted from close range three minutes after the break.
Kilmarnock were sharp in possession throughout without cutting their hosts open too often but did enough to maintain their four-point lead over Motherwell. The result left Kenny Shiels without a win in seven games as interim manager but the Kilmarnock fans chanted 'Kenny must stay' as they enjoyed their team's possession play.
The game also saw Alexei Eremenko end his Killie career - the Finn is suspended for the visit of Rangers - and he went into the bottom tier of the South Stand after the game to throw his boots up to the away fans.
Apart from replacing Jones with the absent Jamie Murphy, Motherwell manager Stuart McCall played a team and formation that he looks likely to start with against Celtic in the Scottish Cup final.
Steven Saunders and Stephen Craigan came into defence following the 4-0 defeat by Dundee United and Tom Hateley lined up in the base of a five-man midfield with John Sutton starting up front on his own.
Despite the extra body in the middle of the park, Motherwell found it difficult to get the ball off Killie at times but they also enjoyed good spells and earned a Hampden send-off from their fans.
Derby manager Nigel Clough, who has been linked with a move for Kilmarnock captain Craig Bryson, was at Fir Park to see Motherwell, who had shipped nine goals in two games, take an early lead.
Jones cut in from the left and hit a powerful right-footed shot which wrong-footed Cammy Bell and bounced inside the near post. Tim Clancy had tried to block the shot and may have got a deflection as Bell dived the wrong way.
Motherwell's other winger, Chris Humphrey, threatened from long range and with a ball across the face of goal before Kilmarnock came into the game.
Aubameyang, who was booked for a reckless challenge on Saunders, saw a header cleared off the line by Hammell and Eremenko had a shot from a tight angle saved by Darren Randolph after Bryson had dispossessed Hateley.
Bell blocked bravely from Sutton after Craigan's long ball before being beaten again in the 38th minute, but the offside flag came to his rescue.
Steve Jennings appeared to run on to Humphrey's cross to head in off the post but made no protest against the decision.
Kilmarnock were enjoying some good possession but could not break their opponents down until just after half-time. Eremenko cut the hosts open with a pass inside Saunders and Dayton cut the ball across the six-yard box for Aubemeyang to slide home.
McCall brought on Francis Jeffers for Jones in the 57th minute and Motherwell picked up the pace. Kilmarnock were fortunate to see Humphrey's cutback evade a home player before Sutton had a shot blocked from a good position.
Killie soon regained the edge. Dayton shot wide from 20 yards, Randolph tipped over Bryson's effort, which looped off a Motherwell defender, and then held Aubameyang's header.
Kilmarnock added Mehdi Taouil to their creative armoury but Motherwell came close when Shaun Hutchinson met a Jennings cross, Bell diving low to stop.
Randolph blocked from the overlapping Garry Hay as both teams sought a winner in vain.