The Cavs took the lead barely a minute into the game with an Evan Mobley three-pointer, and never gave it up in a thoroughly comfortable night for the red-hot Ohio franchise.
Former NBA Most Valuable Player Harden, who was brought in from the Los Angeles Clippers this month, has never won a championship despite being one of the most decorated players in the league.
That was a key factor in his move to the seemingly playoff-bound Cavs, where he has only suffered one loss across seven games, and "The Beard" excelled again, providing four assists against the Knicks.
"We're working to build something special, and each game is an opportunity to get better," said Harden. "Tonight was a good step for us."
They drew level on 37 wins and 22 losses with the Knicks - third in the Eastern Conference - who were poor with their shooting accuracy, making just 11 points in a shocking third quarter.
Around the league
Elsewhere, Anthony Edwards poured in 34 points as the Minnesota Timberwolves earned a hard-fought 124-121 win against the Portland Trail Blazers.
Edwards - MVP at this month's All-Star Game - managed 25 of his points in an explosive first half.
The Charlotte Hornets beat the Chicago Bulls 131-99, with rookie Kon Knueppel racing to his 200th three-pointer.
Aged 20, the Hornets prodigy is the fastest player to reach that mark in NBA history, requiring just 58 games.
Tyrese Maxey sank 32 points plus nine rebounds and eight assists as the Philadelphia 76ers beat the Indiana Pacers 135-114.
The Pacers reached last year's NBA Finals, but have struggled badly this campaign, sinking to the very bottom of the East.
Congolese forward Jonathan Kuminga scored 27 points on his debut for the Atlanta Hawks in a 119-98 win over the Washington Wizards.
The Western Conference-leading Thunder racked up another win, seeing off the Toronto Raptors 116-107.
And the Boston Celtics consolidated their grip on second spot in the East with a 97-81 win over the Phoenix Suns.