Goffin was taking on home hope and World No.137 Robin Haase who is a two time singles winner and former World No.33. He got off to the worst possible start losing the first set 6-3.
He recovered though and took a tight second set 7-6 (7-5) before edging through the last set 6-4 as the number four seed continues on.
Carreno Busta was playing his compatriot Roberto Bautista Agut who is of course ranked higher and he came through a closely fought tie.
He took the first set 6-4 but couldn't follow this up with the World No.30 losing the second set 6-2 before the deciding set went to a tiebreak with the latter edging past and through to the next round.
Simon was making his 11th appearance in Rotterdam and he showed his experience winning through 7-6, 3-6, 6-3 improving his head to head over Mikhail Kukushkin to 4-0. He will next face defending champion Gael Monfils who was in the winners' circle in Montpellier or Joao Sousa.
The former has reached the semi-finals on three occasions in the past and will be hoping for another good week in Holland.
Gilles Simon | 2 | 7 | 3 | 6 | |||||
Mikhail Kukushkin | 1 | 63 | 6 | 3 | |||||
Pablo Carreno-Busta | 2 | 6 | 2 | 7 | |||||
Roberto Bautista Agut | 1 | 4 | 6 | 64 | |||||
David Goffin | 2 | 3 | 7 | 6 | |||||
Robin Haase | 1 | 6 | 65 | 4 |