World number 121 Polansky reached the second round for a third straight year, upsetting Australian world number 52 Matt Ebden 7-6 (7/3), 6-4.
As in 2017, when he ran into Roger Federer after winning his home opener, Polansky could again face a Grand Slam champion, with Novak Djokovic lying in wait should the Serb overcome Chung Hyeon.
Raonic sent over his 15th ace as well as a double-fault as he served for the win against 10th seed Goffin, who had no answer to the Canadian's big game.
The Belgian sent a return long to hand Raonic a match point, with the Canadian finishing it all off on his first chance as Goffin sent a forehand into the net after an hour and a quarter.
"It was tough, I was fortunate to find a way to win today," Raonic said. "I was not sure how it would so - I'm glad it went the way it did." The Canadian had to fight to secure the second set, having saved three break points as he served for the opener.
"I'm glad to have gone through that. I'm also glad he didn't make any returns. This was a good win, but there is another match coming which will create a lot of problems for me.
"Right now, I'm happy with how things are going." In other matches after the bad weather passed, 11th seed Diego Schwartzman crushed Kyle Edmund, the lone Brit in the field after the withdrawal of Andy Murray, 6-1, 6-2.
- Bad weather -
Jack Sock, who has not won a match since before Roland Garros more than two months ago, lost in the first round for a fourth straight event, going down 6-3, 3-6, 6-3 to Daniil Medvedev.
Benoit Paire reined in his fearsome temper to earn a straightforward first-round win after a costly outburst on court last week.
Paire exploded in anger last week during a first-round Washington loss to Marcos Baghdatis, destroying three racquets and earning a massive fine of $16,500 (14,300 euros).
Nadal leads the draw with holder Alexander Zverev, the weekend champion in Washington, the second seed.
Belarusian qualifier Ilya Ivashka extended his run of weekend success as he beat Japan's Yuichi Sugita 6-2, 6-3. Pablo Carreno Busta advanced when Japan's Yoshihito Nishioka retired after the first set.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)