The German Deutsche Bahn has an InterCity bus-line from Düsseldorf through Maastricht to Liege. The bus goes back and forth twice a day and only stops in those 3 cities. The bus has free onboard WiFi and a free entertainment portal, power outlets at the seats and you can even use a BahnCard to travel with a discount. You can use one ticket for their entire journey by IC Bus and by Deutsche Bahn train.
The bus stops at the new international bus station in Maastricht. This is next to the train station on the side furthest from the river. To reach the bus station from the train station, go up and over the tracks, and walk down the stairs on the Meerssenerweg side. Once outside, walk past the bike racks and the P+R carpark. Keep walking until you reach the bus shelters, which will have signs displaying information about the international buses arriving soon.
The bus goes to Düsseldorf ZOB bus station and to the bus stop at the Liege-Guillemins train station. According to their schedule, the Bus will go from Maastricht to Liege daily at 12:25pm and 06:25pm. It will arrive approximately 40 minutes later in Liege. If you intend to go from Maastricht to Düsseldorf, you can catch the Bus at 08:20am and 02:50pm. The journey will take about one and a half hours.
Prices start from 9€ from Maastricht to Düsseldorf and from 7€ from Maastricht to Liege. In order to book a ticket and reserve a seat, as well as finding exact times and prices download this flyer and visit their website.