But Australian sixth seed Bernard Tomic became the first seed ousted at the hardcourt event.
But Australian sixth seed Bernard Tomic became the first seed ousted at the hardcourt event, with Belgian qualifier Steve Darcis rallying to deliver a 3-6, 6-1, 6-4 defeat to the world number 31.
And 37-year-old second seed Ivo Karlovic followed shortly thereafter, falling 7-6 (7/5), 7-6 (7/3) to 69th-ranked American Donald Young despite 19 aces from the world number 20 Croatian.
Raonic, who had beaten Smyczek in the first round of the 2015 US Open in their only prior meeting, booked a second-round matchup with 49th-ranked Croatian Borna Coric, who eliminated Colombia's Santiago Giraldo 6-2, 6-3.
World number four Raonic is seeking a ninth career ATP crown. He has won at least one title in each of the past six years and last year reached his first Grand Slam final, losing to Britain's Andy Murray at Wimbledon.
Darcis, ranked 57th, faced only one break point over the final two sets in fighting back to bounce Tomic in 90 minutes, booking a second-round match against either Germany's Tommy Haas or Georgian Nikoloz Basilashvili, who lost Sunday's ATP Memphis Open final to American Ryan Harrison.
US third seed Jack Sock fired eight aces in downing Moldova's Radu Albot 6-4, 7-6 (7/2). Sock, ranked 21st, next plays Spain's Guillermo Garcia-Lopez, who dispatched Germany's Dustin Brown 6-3, 6-3.
Argentina's Juan Martin Del Potro and Haas will launch comeback bids in later matches.
Haas underwent right foot surgery last April and had not played since October 2015 until retiring from a first-round Australian Open match last month.
Del Potro, the 2009 US Open champion, starts his 2017 campaign against South African Kevin Anderson after skipping the Australian Open to better regain fitness after helping Argentina win the Davis Cup last November.
Del Potro won the Delray Beach title in 2011 and Anderson took the 2012 crown.