Following a goal after just 19 seconds from Greig Stewart, Hibs responded with goals from Griffiths, Doyle and Wotherspoon before Jon Robertson made sure of a nervy finish for the SPL side as they desperately held on to the victory.
Captain for the day Ivan Sproule admitted that his side were the underdogs for the day against their Division Two opponents.
“Cup ties are never easy, so coming here we knew they were riding high in their league and we were playing on an awkward pitch. So we’ve come through that and the most important thing is to get through into the next round and we’re in that.
“A few people maybe had us written off and Cowdenbeath as favourites before the game, so it’s just nice to get through into the next round.”
With Hibs sitting in 11th place in the SPL the winger admitted also that there was an added amount of pressure to succeed in the game against Cowdenbeath.
“There is always pressure whenever you’re down and around the bottom of the league. And it is always in the back of your mind when you’re playing cup ties.
“But we’ve gone out their today knowing that the performance wasn’t the main thing, the main thing for us was to get through into the next round.
“The performance will need to be bigger and better next week as we play against Dunfermline, especially because that’s the one we have our eye on now as we’ve got that one (Cowdenbeath) out of the way.”
With Hibernian firmly engaged in a relegation battle with Dunfermline the match next week takes priority over everything else for the squad as they attempt to fight for their SPL survival and Sproule admitted that the fans deserved better.
“The game today was not against SPL opposition, but a win is a win and when you’re not getting wins you have to take something out of it.
“There was a big, large travelling support here today for Hibs and you know hopefully the manager can add to the squad and keep the rest of us on our toes.”
Leigh Griffiths is also on loan at Hibs until the end of the season as the club revealed on Friday before the Scottish Cup tie. The striker netted his 5th goal for the team he supported growing up and Sproule has high expectations of the 21-year old by comparing him to Steven Fletcher.
“He can score goals like the one today or he can drive you mad! In a way he reminds me a wee bit of Steven Fletcher because Fletch used to score goals that made you stand back and go ‘that was special’.
“Sparky does that in training and he brings that to us in the game and he is the kind of player that the club needs to keep and to push on.
“He is already a popular figure with the fans because he is a Hibee, and if he keeps on scoring goals like that and his attitude for the club has been great and he has got that bit of fire that fans like and he has been a breath of fresh air since we brought him to the club.
“If he is going to be as big as Fletch, only Leigh can tell you that and only Leigh can do that.”
Hibernian are in the pot for the 5th round draw which is made today at 2:30 by Andres Villas-Boas and Marcelo Lippi.