Eoin Doyle’s strike proved enough to secure a first win at Easter Road for Hibernian since September and send the Edinburgh side into the last eight of a competition they have not won in 109 years.
But it was the defensive resilience which proved most pleasing for manager Fenlon, as the often-maligned Hibs back line remained firm.
Stand-in captain James McPake was imperious, and Paul Hanlon appeared to revel alongside the on-loan Coventry man.
Deadline-day arrivals Matt Doherty and Pa Kujabi were also excellent on their debuts, while the midfield and attack were defensively diligent.
It was a notable progression for a Hibernian side who had conceded 14 goals in five matches prior to this encounter and had not registered a clean sheet at home since September.
Fenlon said: “It’s great to be through and I thought we showed great character and defended really well as a team.
“The players deserve the credit — they put in the shift and got the reward.
“From the front two right through to the goalkeeper we were determined. We got the early goal and it really gave us something to hold on to.
“It’s my first clean sheet, and it’s something we’ve spoken about. If you keep clean sheets you’ve got a great chance of winning matches. It’s something we can build on.”
Hearts and St Johnstone will meet again after drawing 1-1 at Tynecastle yesterday.
Hearts struggled to build on the advantage created by winger David Templeton’s 10th-minute goal.
And, after Francisco Sandaza headed against the bar and Dave MacKay was sent off for two bookable offences, Cillian Sheridan equalised for 10-man Saints after 77 minutes.
Elsewhere, Aberdeen, who have made a habit of going out of cup competitions to lower-league opposition, looked set for another shock when Scott McLaughlin broke the deadlock for Queen of the South.
However, Scott Vernon spared Aberdeen’s blushes with a close-range equaliser to earn the Dons a replay.