The teams meet at Easter Road with the home side hoping to continue their good recent run.
After a difficult start to the season, which produced four straight defeats, the Edinburgh club are now unbeaten in their last four games in the Scottish Premiership.
Hibs have raced up to fifth in the table and Fenlon said: "It is difficult to win games at home in this league so we have to try to make sure we build that little bit of momentum after picking up our first three points here.
"We've got a cup game to look forward to now and it gets us into the quarter-finals as well, which is nice.
"The confidence is building. We've had a couple of good wins - on the road at St Johnstone and then at home to St Mirren.
"We are unbeaten in a few games now and that gives everybody a lift and there's a decent atmosphere around the place at the moment."
The Hibs manager also believes a good run in the cup is good for the club's coffers, saying: "We were disappointed to get knocked out of the League Cup early last year so we'd love to go on a little run.
"The runs in the Scottish Cup in the last two years have helped from a financial point of view. It's also another game won, which helps confidence, and it's another game to look forward to financially."
As for Tuesday's opponents, he added: "We've watched three of their games and plenty of DVDs and they are a good side.
"They've got some good players who work tremendously hard for each other.
"We know we are going to have to play well. They come here with nothing to lose and we are going to have to play well to get through."