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.
Until the end of 2019, the IC bus will be stopping at the Groene Loper instead of the station. This is because there is a new proper international bus station being built on the Meerssenerweg, and until that is done, all international buses are using different stops.
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 and 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 and you will be traveling for 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.