Defeat left United seventh and five points adrift of the top four finish
Chelsea supporters taunted Manchester United manager Jose Mourinho with chants of "You're not special anymore!" as his Stamford Bridge return yielded a humiliating 4-0 defeat on Sunday.
With seven major titles across two spells, Mourinho is Chelsea's most successful ever manager, but his return to his old stomping ground ended in one of the most chastening results of his career.
Pedro Rodriguez opened the scoring after just 30 seconds and Chelsea did not look back, Gary Cahill, Eden Hazard and N'Golo Kante completing an emphatic Premier League victory.
"We scored the early goal, but we continued to play good football and create many chances," Conte told the BBC.
"Today we didn't concede, which was important. It was a type of win that increases the confidence."
It was a fitting tribute to former Chelsea vice-chairman Matthew Harding, whose death in a helicopter crash 20 years ago was marked prior to kick-off with banners and a giant flag.
Conte's side have won three consecutive league games without conceding a goal and climbed to fourth place, just a point below leaders Manchester City, Arsenal and Liverpool.
Mourinho has already tasted defeat three times in the league with United, who trail City by six points ahead of Wednesday's Manchester derby in the League Cup.
"We made incredible defensive mistakes, individual mistakes, and you pay for that," Mourinho told Sky Sports.
He refused to divulge what he had said during a terse exchange with Conte after the final whistle, saying: "My words with Antonio Conte were for him, not for you."
Mourinho was said to have been irritated after Conte encouraged the home fans to make more noise following Chelsea's fourth goal.
Mourinho also expressed fears that Eric Bailly had sustained a "really bad" knee ligament injury after the Ivorian centre-back was forced off early in the second half.
The team sheet told a tale of two captains: United's, Wayne Rooney, was absent after reportedly injuring his thigh, while Chelsea's, John Terry, remained on the bench following an ankle injury.
Mourinho was greeted warmly by Terry and former assistant Steve Holland prior to the game, sharing a warm embrace with the former, but Chelsea's hospitality vanished within 30 seconds of kick-off.
Chris Smalling inexplicably allowed Marcos Alonso's pass from Chelsea's left to bounce past him and Pedro nipped in to round United goalkeeper David de Gea and roll the ball home.
Mourinho, sacked for the second time by Chelsea owner Roman Abramovich last December, looked faintly shellshocked.
He saw his side squander a chance to level when Zlatan Ibrahimovic headed over after Antonio Valencia had stood up a cross from the right.
More slack defending allowed Chelsea to double their lead in the 21st minute, Cahill slamming home after Hazard's corner had struck Ander Herrera and bounced down inside the six-yard box.
A pocket of Chelsea fans beside the dug-outs turned Mourinho's 'Special One' nickname back on him, chanting: "You're not special anymore!"
Chelsea goalkeeper Thibaut Courtois had been relatively untroubled up to that point, although he produced a smart double save to repel Herrera's left-foot effort and Jesse Lingard's follow-up.
It was an ideal first half for Chelsea, but David Luiz was fortunate to escape with only a yellow card after planting his studs in Marouane Fellaini's knee five minutes before half-time.
Mourinho changed tack at half-time, sending on Juan Mata for Fellaini and moving Marcus Rashford up front alongside Ibrahimovic in a 4-4-2 formation.
Lingard sought to sound the revolt for United, wriggling away from a pair of Chelseaplayers and unleashing a crisp drive that Courtois had to push away.
But in the 62nd minute it was game over. Nemanja Matic's pass down the inside-left channel found Hazard, who checked inside Smalling and steered a shot into the bottom-right corner.
Kante completed the rout, darting between Smalling and the sleep-walking Paul Pogba to tuck away his first Chelsea goal since his close-season switch from Leicester City.