Kyrie Irving scored 27 points while LeBron James added 24 as the Cavaliers dominated almost from start to finish to the delight of their home fans at the Quicken Loans Arena.
The 31-point rout was Cleveland's biggest ever victory in a playoff game.
The Cavaliers went into the game well-rested after wrapping up back-to-back 4-0 sweeps in their opening two postseason series.
Toronto by contrast had been forced to make a quick turnaround after only clinching a 4-3 series victory over the Miami Heat in their conference semi-final on Sunday.
On the evidence of Game One, few would bet against James and the Cavaliers making short work of the Raptors.
Russell Westbrook inspired a second-half fightback as the Oklahoma City Thunder came from behind to beat the Golden State Warriors 108-102 in the opening game of the Western Conference finals on Monday.
Westbrook poured on 27 points as the Thunder overturned a 60-47 halftime deficit to snatch victory in a pulsating clash between two of the most potent attacking units in the NBA.
Westbrook also chipped in with 12 assists and six rebounds while team-mate Kevin Durant finished with 26 points as the visitors silenced the Golden State home crowd at the Oracle Arena.
Game Two in the best of seven series takes place in Oakland on Wednesday.
After a stunning upset of the San Antonio Spurs, can the Thunder keep their success going against the defend champions? The match-up is filled with star power with two-time reining MVP Stephen Curry on one side and OKC’s duo of Kevin Durant and Russell Westbrook on the other.
In the East, can the Raptors slow down the Cavaliers and avoid becoming the third victim of a Cleveland sweep? LeBron James and Co are well rested heading into the match-up, while Toronto were taken seven games in each of the first two rounds.
Listen to our analysis and breakdown of both series, as well as predictions on which two teams will meet in the Finals.