Having won the Open Sud de France in Montpellier last week, Monfils needed only 70 minutes to dispatch his Portuguese opponent, firing five aces and converting four break points.
The 33-year-old Frenchman, who is looking to become the first player to win back-to-back Rotterdam titles since Sweden's Robin Soderling in 2011, next faces compatriot Gilles Simon who beat Mikhail Kukushkin 7-6(3) 3-6 6-3.
"It's never easy to come back after a win," Monfils said. "But I have great memories from last year."
In an all-Spanish showdown, Pablo Carreno Busta beat sixth seed Roberto Bautista Agut 6-4 2-6 7-6(4) to qualify for the quarter-finals after a battle lasting nearly two-and-a-half hours.
Carreno Busta fired 11 aces and saved seven break points to advance at his higher-ranked compatriot's expense.
Goffin will face Italian Jannik Sinner, who was awarded a walkover after his opponent Radu Albot withdrew.
Top seed Daniil Medvedev is in action later on Wednesday when he faces Canadian Vasek Pospisil in the first round.
(Reporting by Rohith Nair in Bengaluru, editing by Ed Osmond)