Elisabetta Grillo, 41, who also accused the celebrity couple of lying under oath, told jurors Ms Lawson permitted the teenagers to smoke the Class C drug as she gave evidence in her fraud trial.
The defendant, who along with her sister Francesca Grillo, 35, is accused of spending £685,000 on credit cards belonging to the celebrity couple to buy designer goods and luxury holidays for herself, made the allegations as she spent a second day in the witness box at Isleworth Crown Court in west London.
Elisabetta, 41, was asked by prosecutor Jane Carpenter to explain a duty-free transaction for £69.71 in New York in June 2010.
"It was cigarettes for the children. I bought them and Nigella allowed me to buy them," Grillo said.
"I don't remember how many packs. Nigella always told me to buy it."
Asked by Ms Carpenter: "What on earth did you think you were doing, buying cigarettes for underage children?"
Grillo said: "Well, if Nigella Lawson let the children smoke weed..."
The defendant tailed off as Judge Robin Johnson interrupted the exchange.