The Scottish First Division side had produced the result of the round this time last year when they sent Hibernian crashing out of the competition but there was to be no shock this time as Sammon netted either side of the break after the Greenock outfit had restored parity through Ryan McGuffie.
Kevin Kyle then put the gloss on Tuesday night's win at Rugby Park late on, hours after being plucked from the international wilderness when he was named in George Burley's Scotland squad for next month's World Cup double-header against Macedonia and Holland.
Alan Combe was back in the Killie goal for the first time this season at the expense of Cammy Bell after a hip problem had kept him out of the opening two games in the Scottish Premier League.
The first real chance fell to Morton when Jim McAlister ran onto a short corner from Kevin Finlayson and bore down on goal but the end product was poor and Combe comfortably blocked at the near post.
At the other end, Ryan McWilliams was called into action when Kyle collected a long ball from Craig Bryson before turning in the box and unleashing a powerful strike which left the Morton goalkeeper's palms stinging.
The big striker was threatening again when he threw himself in front of a cross from the right from Mehdi Taouil only to nod just wide of target.
Killie looked most likely the open the scoring and the breakthrough came after 24 minutes when Sammon was tripped in the box by McWilliams and referee Mike Tumilty immediately pointed to the penalty spot.
Sammon brushed himself off and stepped up to rifle home a right-footed shot which left McWilliams no chance in the Morton goal.
Just when the home side thought they would be heading into the interval with the advantage, their First Division visitors hauled themselves level with a minute of the first half remaining with a penalty of their own.
This time, Brian Graham was fouled in the box by Tim Clancy and McGuffie did the honours from the spot, sending a confident, low strike past Combe.
Unsurprisingly, Morton emerged for the second half full of confidence and had a couple of decent half-chances after the restart, as the home crowd grew increasingly restless.
But Killie were back in front with 64 minutes gone when Sammon grabbed his second of the night. The ball broke kindly for Kyle and he whipped across the face of goal where Sammon was waiting to direct a header past McWilliams from close range.
Taouil then tried to kill off any chance of another Morton comeback with a well-struck effort which rippled the side-netting, before substitute Manuel Pascali - who had replaced the injured Jamie Hamill at the break - just failed to connect with a Bryson cross just a few yards out.
Sammon then blasted over from the edge of the six-yard box when it looked easier to leave the net bulging and claim his hat-trick.
Instead, it was Kyle who had the final say when he met a David Fernandez cross and nodded home from close range to seal the win.