It was relatively comfortable come the end but for a spell early in the second half, when Stranraer scored twice in quick succession to narrow Hibs' lead to 4-3, it began to look as if an upset could well be on the cards.
Having just emerged from a sticky patch to string together a five-game unbeaten sequence, defeat to a League One side could have plunged Hibs back into the pits of despair. A fifth goal, however, finally killed off Stranraer's plucky resistance and it is Pat Fenlon's side, and not the feisty underdogs, who progress to the quarter-final draw.
Stranraer had posted their intentions with an early goal but Hibs recovered strongly from that setback and by the 48th minute they were 4-1 to the good and seemingly coasting to a straightforward win.
Defensive lapses, however, let the visitors back into it and suddenly there was tension in the air once more. Chris Aitken reduced the deficit with a terrific shot from the edge of the box that even drew a generous burst of applause from the home side, and three minutes later Stranraer scored again, Michael Nelson powering Aitken's corner past his own goalkeeper with an unstoppable header in the wrong direction. That send audible moans of discontent echoing around Easter Road but Hibs nerves would be settled again shortly after when Liam Craig stroked home a penalty, completing his hat trick in the process.
Even then, Stranraer did not throw in the towel. Aitken, who had a busy night in midfield, lashed in another shot that drifted only narrowly wide and then watched his header land on top of the Hibs net rather than inside, before Frank McKeown lumbered forward from defence only to shoot well wide of goal.
Stranraer's commitment to attack never wavered and, although they failed to add a second Premiership scalp after beating Ross County in the previous round, manager Stephen Aitken could not fault his players.
"I really enjoyed it," he said. "Although we got beat I'm really proud of the players, especially in the second half. At 4-1 it could have been difficult but they rolled their sleeves up and dug right in. If we had stayed a bit longer at 4-3 it might have been a different game. The players sensed they had a wee chance at that point and on another night it could have been different. People have criticised us when we have been too negative and now we are getting criticised for being too attack-minded. You can't win."
It is Hibs, though, who are still in the competition and there was plenty to admire in some of their attacking play, even if they looked vulnerable defensively at times.
They like their cult heroes to come with a swagger at Easter Road and in Abdellah Zoubir they may well have another who will get them out of their seats this season. This was a first start for the Frenchman who signed on a year-long loan from Istres in Ligue 2 just before the close of the transfer window and he did not waste his opportunity, showcasing a number of tricks and some fancy footwork.
He embroidered his performance with Hibs' second goal of the night, a deflection taking his shot over the unfortunate goalkeeper as Easter Road rose to acclaim him. "He's different to what we've got and this was a good game to get him into tonight," said Fenlon. "I think the supporters will enjoy him over the course of the season. In the first half in particular we got him a lot on the ball and he's difficult to play against. He's got very good feet, his balance is good and he's strong."
It was Craig, though, who was selected as the man-of-the-match after bagging his first ever senior hat-trick. The first was an equaliser on nine minutes - after Jamie Longworth had silenced Easter Road by heading Aitken's corner past Ben Williams to give Stranraer a shock lead - the midfielder making a well-timed run into the penalty box to connect with Rowan Vine's cross.
His second, Hibs' fourth, came early in the second half, the former St Johnstone player breaking clear of the Stranraer defence to poke a shot past David Mitchell, before he then pinched the ball from James Collins to net from the penalty spot after Scott Rumsby was adjudged to have handled. Rumsby was one of the few Stranraer players who will not look back on this night with any great fondness, the defender also scoring Hibs' third goal when he slid Vine's cross beyond his own goalkeeper.
"There were a lot of chances in the game at both ends; it could have finished 7-6," added Fenlon. "But we're delighted to be in the next round. We reacted well to losing the early goal but the confidence is in them right now and you can see that from how they came back from that early setback."