Chris Burke also netted his first goal for Lee McCulloch’s men as he scored the opener just after half-time.
Kris Boyd and Erwin, who only completed his move from Leeds on Friday, then wrapped up the win which sees the Rugby Park men into the second round as one of the four best-placed group runners-up.
Killie knew a win was imperative if they were to escape Group E following their loss to local rivals Ayr in their opening match.
But they were fortunate to have Jamie MacDonald in alert mood after 29 minutes, with the keeper’s reaction stop rescuing Iain Wilson after he turned a Mark Stewart cross towards his own net.
And luck was on Killie’s side again a minute later as Danny Handling got his head to Chris Johnson’s corner. His attempt looked to be a good foot over the line before MacDonald clawed it away but referee Bobby Madden refused to sanction the goal.
The hosts returned after the break with a far more urgent look about them and got their reward within eight minutes of the restart as Burke nodded home from Dom Thomas’ delicious cross.
New Kilmarnock recruit Erwin was handed his debut after coming on for the goalscorer on the hour mark but it was the man he is aiming to replace in the Rugby Park line-up who doubled their lead, with Boyd bulleting home with his head from another Thomas centre.
However, Erwin did add his name to the scoresheet with 12 minutes left, as the former Motherwell man clipped his debut strike in off the post after Boyd had helped on a Jordan Jones cross.