Profit after tax increased to £132 million ($173.4 million, 151.6 million euros) in the six months to the end of September compared with £93 million a year earlier, Burberry said in a statement.
Revenues fell three percent to £1.22 billion, offset by cost savings of £80 million.
Gobbetti is shaking up the brand with a strategy overhaul that aims to add even more luxury to the fashion house's products, which include its famous trench coat.
One of his first moves was to appoint Tisci.
Burberry confirmed its outlook for its 2018-19 financial year, which includes total cost savings of £100 million.
Tisci's debut show came at London Fashion Week in September, where the Italian designer presented Burberry's 2019 spring/summer collection.
Tisci broke with the label's tradition by presenting a range of evening dresses.
Meanwhile on Thursday, Burberry's share price gained 0.7 percent to £18.28 on London's benchmark FTSE 100 index, which was up 0.4 percent overall.