Dort, midway through the fourth quarter at Rocket Mortgage FieldHouse, drew a foul fighting for a loose ball with Love and Darius Garland near halfcourt.
After the official blew the play dead, Dort threw his right elbow in what appeared to be an effort to shake Garland and Love off of him, but he drilled Love directly in the shoulder near his neck.
That set Love off, and sparked an altercation.
Officials eventually hit Dort with a flagrant two foul, which triggered an automatic ejection.
Dort finished the night with 10 points and one assist in 32 minutes. He is averaging 16.2 points and four rebounds per game so far this season, his third in the league. The 22-year-old, who played his entire rookie season on a two-way contract, is in the third year of his initial four-year, $5.3 million deal with the Thunder.
The Cavaliers, after a tight first half, flew ahead in the third quarter and used a quick 13-3 run to grab a double-digit lead, their largest of the game at that point. The Cavaliers then held the Thunder to just two field goals in the first half of the fourth quarter, though both of them came within two feet from the rim, and held on to claim the seven-point win.
Garland led Cleveland with 23 points and 11 assists in the win, which marked its seventh win in nine games. Love finished with six points and six rebounds in 23 minutes off the bench.
Shai Gilgeous-Alexander led the Thunder with 29 points and nine rebounds while shooting 12-of-23 from the field. Oklahoma City has now lost 12 of its last 14 games.