The 25-year-old gave the Blue-White the lead in the 37th minute, after heading Alejandro Pozuelo's cross past Marvin Schwaebe.
And before the break, Leandro Trossard doubled the lead from the penalty spot for the hosts after John Larsson handled the ball in the area.
Two minutes after second-half action resumed, Hjoertur Hermannsson restored the Danish club’s hope firing past Danny Vukovic.
The visitors levelled the scoreline in the 51st minute through Kamil Wilczek.
However, Samatta turned the Brondy Stadium outfit's parade sour four minutes later, powering a header past Schwaebe and with just 20 minutes of action left, he completed his treble.
Trossard added the icing on the cake in injury time.
Samatta featured for the whole duration, while Congo DR’s Dieumerci Ndongala was substituted for Paintsil in the 74th minute and the Ghanaian Joseph Aidoo was an unused substitute.
Genk host Waasland-Beveren in their next Belgian top-flight outing at the Luminus Arena on August 26.