Purcell knocked out world No.7 Casper Ruud and three-time grand slam champion Stan Wawrinka in last week's run to the quarter-final of the Cincinnati Open, before pushing world No.1 Carlos Alcaraz deep into a third set.
With all that behind him, the in-form 25-year-old Sydneysider made a fast start against Cecchinato in North Carolina, breaking him in the opening game to secure an advantage he never let slip.
Purcell, playing his first match as a top-50 ranked singles player, raced into a 4-0 second set lead before progressing 6-4 6-1 in 68 minutes.
In the second round Purcell, now a career-best 47th in the world, faces Finland's Emil Ruusuvuori, who was beaten by Alexei Popyrin in the last 16 in Cincinnati last week.
The 56th-ranked Finn knocked Purcell out of this year's Australian Open and also won their only other match, a qualifier three years ago.
Purcell, though, is in the form of his life having won nine of his last 11 matches - beaten only by Alcaraz and, in Toronto, triple grand slam champion Andy Murray.
Fellow Australian Rinky Hijikata is also through to the second round, recovering after dropping the first set to beat Ukraine's Illya Marchenko 4-6 6-3 6-2.
Hijikata's reward is a second-round meeting with the tournament's top seed, world No.29 Borna Coric of Croatia.
