Two goals in three second-half minutes from Jamie Hamill and David Silva sent Paatelainen's Ayrshire side into the quarter-finals and nullified controversy over Willie Collum's decision to reverse a first-half penalty award for the hosts.
Jonathan Grounds gave Hibernian an early lead but Kilmarnock soon levelled when Hamill netted on the rebound and the right-back later converted a penalty to continue a miserable run for the visitors, who have now won just four times in 26 matches.
Paatelainen's successor, John Hughes, had appealed to the Hibs fans to back the team after they were booed off following Saturday's home draw against Hamilton, and they were cheering in the eighth minute when Grounds netted.
Kilmarnock charged down three attempted shots outside their box, but that left a gap brilliantly exploited by the composed Liam Miller, who laid the ball into the path of Grounds to fire into the far corner.
Hibs remained on top and Derek Riordan released John Rankin with an excellent first-time pass, but the midfielder's first touch allowed Cammy Bell to come off his line and block.
Kilmarnock only sparked into life midway through the first half when Harry Forrester struck a powerful 25-yard strike, which Mark Brown pushed over.
Grounds almost carved out a second goal when his diagonal ball found Colin Nish and, although the striker's touch got away from him, the ball fell to Edwin De Graaf who saw his low shot blocked by Bell from 12 yards.
The on-loan Middlesbrough defender returned the ball and Nish looked set to score but he headed back across goal after Miller got in his way.
Hibs had a huge let-off in the 24th minute after Collum instantly pointed to the spot when Sol Bamba went to ground and brought down Sammon as they chased a through ball.
But, after a discussion with fourth official Bobby Madden and assistant Martin Cryans on the halfway line, the referee gave a corner.
Hibernian's reprieve lasted just five minutes though. Sammon turned his man in the box after collecting Ben Gordon's low cross and Hamill slid the ball into the corner after Brown had saved well from the Irishman. Killie continued to improve but Alexei Eremenko twice fired well over from the edge of the box.
Hibs started the second half well and appealed for a penalty when the grounded Hamill appeared to stop Riordan's effort with his hands.
De Graaf then sliced wide of an open net from 10 yards after Bell had got down well to parry Riordan's deflected volley.
Hibs continued to press and Bell saved from Nish after the striker had helped on Kevin McBride's header. The striker then had a header cleared off the line but Killie quickly broke following the corner to leave them with three on one.
Sammon took out Michael Hart by slipping the ball inside for Craig Bryson, who only had Brown to beat, but his first touch was too heavy and the Hibs goalkeeper smothered.
Kilmarnock soon hit Hibs on the break to better effect when Sammon released Forrester inside the box and he drew a foul from Francis Dickoh, who slid in needlessly.
Hamill tucked the penalty into the corner and the hosts soon finished the tie in the 74th minute when Silva cut inside from the left wing and fired a low shot that Brown let in at his near post despite getting a hand to it.