The opener, who recently signed a two-year County contract that will begin next summer, made 51 on the first day of the Specsavers County Championship Division Two clash.
Northants eventually made their way to 255 all out, with Saif Zaib top scoring with 57.
Derbyshire finished the day on 60 for two, with Brett Hutton and Ben Sanderson bagging a wicket apiece at the County Ground.
And Curran said: “It was nice to get some runs. I managed to get in today which I haven’t done previously and I should have really gone on.
"I think 250 is perhaps a little below par so we need some early wickets in the morning.
“The wicket did a bit, it swung throughout so you have to be patient with the ball."
Derbyshire face a difficult task as they look to claim a first-innings lead.
And bowler Hardus Viljoen said: "It seems like a wicket where you’re never in, so as a bowler you’ll always be in the game.
"I think we bowled better than the board suggests and now we need a couple of partnerships to get us going on day two.
“As a team we bowled well, Tony (Palladino, who took three for 25) is in a purple patch and we now know what to do with the bat on this wicket."