The Dark Blues welcome County to Tayside knowing they have a 14-point gap to cut at the foot of the table in their attempt to stave off the threat of relegation.
The SPL's bottom club face a stiff test against the Staggies, who have earned themselves a reputation for being experts at shutting up shop away from home.
Smith watched his side defeat Morton 5-1 in the Scottish Cup last weekend and hopes to see them build on that by beating Derek Adams' men.
"County will come here and try to keep things tight so it will be up to us to get the better of them," Smith said.
"They've proved this season that they can be a very difficult side to break down away from home.
"All credit to them for that but we're the home team, and we'll be looking to go out there and get a positive result against one of the teams round about us in the table.
"It will be a very difficult match but we have to believe we can do it and I have faith in these players."
Dundee are desperate to make up some much-needed ground in their fight for survival, but Smith has played down talk of Friday night's game being must-win for the Taysiders.
He said: "Every game is big for us between now and the end of the season.
"It's been like that all season where we've gone into all games focusing on trying to get the three points.
"There is no more added pressure going into this game than there has been in any other one.
"The players have had a good week's training so are really looking forward to the game.
"Our last game against them ended in a draw up there and there was nothing between the two sides.
"We've just got to make sure that whenever we get chances in front of goal we have to take them."
Dundee's confidence is high after sweeping past Morton, which Smith hopes can be a factor on the night.
He said: "It's given the lads a boost. And the goals were spread around as well which is always encouraging from any teams' point of view.
"We want the fans to rally round and really help the boys as they can make so much difference on the night."
Dundee are still without long-term injured players such as captain Stephen O'Donnell (knee), Mark Kerr (knee), Davide Grassi (knee) Jamie McCluskey (Achilles) and Carl Finnegan (knee).