To get a cheaper advance Sparpreis ticket, at least part of your journey needs to be on an IC or ICE train - if the entire journey is on regional trains you may have to pay for a more expensive Flexpreis or a regional ticket.
To get a few more options (assuming you're using the Deutsche Bahn website), add a 00:00 stopover (e.g. at Dortmund Hbf). You may have to untick all the non-IC/ICE travel options for one leg of the journey (i.e. from Dusseldorf Airport to Dortmund Hbf). This can all be done under the 'Change Other Data' tab if you're creating/editing your journey (see 'stopovers' and 'connections').
For example, on the 13th March I can get a journey option for €19.90:
Düsseldorf Flughafen dep 19:00
ICE 645 Intercity-Express Direction: Berlin Ostbahnhof
Komfort Check-in möglich
http://bahn.de/komfortcheckin , Bordrestaurant
Hamm(Westf) arr 20:07
Transfer time 39 min.
Adjust the transfer time
Hamm(Westf) dep 20:46
ERB 89 (90037) eurobahn Direction: Paderborn Hbf
Number of bicycles conveyed limited , ticket machine on train
Paderborn Hbf arr 21:39
It's an advance ticket though so if you miss your IC/ICE train it won't be valid for that leg (but the regional train leg is valid on any service)!