Britain and Belgium meet in the Davis Cup final in Ghent from Nov 27-29 with world number three Murray and Goffin, who eased past Serbian qualifier Dusan Lajovic, set to clash in the number ones’ singles rubber.
Murray needed less than an hour to dismiss the 18-year-old Coric, converting four of his five break points while never allowing his opponent the chance to steal his serve.
Earlier, the 16th-seeded Goffin also needed less than an hour to sweep aide Lajovic 6-2 6-2, converting five of eight break points.
Japan’s Kei Nishikori, the sixth seed, survived a barrage of aces to beat France’s Jeremy Chardy 7-6(4) 6-7(6) 6-1, securing a third-round meeting with another Frenchman, Richard Gasquet.
Chardy fired 17 aces but it was not enough to unsettle Nishikori, who played better on the key points.
The 10th-seeded Gasquet looked solid in a 6-2 7-5 victory against Argentine Leonardo Mayer.
The Paris Masters is the last tournament before the season-ending ATP World Tour finals, which will be played between the eight best players of the season from Nov 15-22 at the 02 arena in London.
World number one Novak Djokovic, Stan Wawrinka, Roger Federer, Rafa Nadal, Nishikori, Murray, Tomas Berdych and David Ferrer have all qualified.