Kante's low swerving effort in the 51st minute beat David de Gea in the United goal and set up a semi-final showdown between Chelsea and Tottenham at Wembley.
The France international put in a dominant display in midfield against compatriot Paul Pogba after Ander Herrera was sent off for two bookable offences in the first half to leave the visitors with a numerical disadvantage.
Lampard was glowing in his praise for Kante, saying there was no better midfield player in the world than the 25-year-old at present.
"I'd go as far to say that he's the best central midfield player in the world on current form, I really would," the former Blues midfielder was quoted as saying by the Daily Mail.
"Looking at the way he's performing this year, he may not be scoring lots of goals but what he's giving to the team in the way he's playing, the driving force that he is, I cannot see anyone else out there in world football better than him at the moment."
Former Newcastle and England striker Alan Shearer said Kante was odds on to be named the PFA Player of the Year for his impressive first season at Stamford Bridge.
The Frenchman was signed by Chelsea from Leicester City for £30m ($36m) in the summer.
"I think you're looking at the Football Writers' Player of the Year and the PFA Player of the Year," Shearer said.
"We are not used to him scoring too many goals but he was absolutely superb, he was all over the park as usual. When United did get the ball back he was straight at them and getting it for Chelsea."