The Canadian, who was recently beaten by Andy Murray in the Aegon Championships final at Queen's, secured a 7-6(4) 6-2 6-4 victory on the grass court at SW19.
Carreno-Busta showed some promise early in the first set as he created two break points at the first time of asking, but the 24-year-old failed to convert them.
Raonic failed to produce a single break point, pushing the first set into a tie-break, which the Australian Open semi-finalist scooped 7-4.
The 25-year-old then began to find his stride as he nabbed a double break before wrapping up the second set in just 29 minutes.
Raonic broke early again in the third, and Carreno-Busta tried to force a comeback as he saved three break points and six match points, but his opponent eventually got over the line.