The former left-arm spinner was appointed to the Andrew McDonald-led coaching staff in May. Vettori's first match in his new role began with the Aussies securing a comprehensive 10-wicket win against Sri Lanka in Galle.
The Pat Cummins-led side have taken massive strides in their pursuit of a spot in the World Test Championship (WTC) final. They have now picked up wins over Pakistan and Sri Lanka away from home.
The team overcame a stiff challenge in Pakistan earlier this year, emerging winners by a slim 1-0 margin on rather flat surfaces.
However, in Sri Lanka, the visitors faced a whole different challenge after being posed with a typical subcontinent wicket. Thankfully, Australia's spinners stepped up to wrap the contest in three days. The team from Down Under are now on the lookout to win the next Test as well, which begins on July 8 at Galle.
Australia will tour the subcontinent for the third time in succession after their ongoing series. The current World Test Championship (WTC) leaders will play a four-match Test series in India early next year, which could potentially decide the fate of the competition.
Believing that conditions in India range from venue to venue, Daniel Vettori said:
"In a lot of ways, it's been nice to have a subcontinent tour of Pakistan, then here [in Sri Lanka] and build towards India. Conditions will be very different. We will get a lot of variation from venue to venue."
"You could get anything in between [the pitches in Pakistan and Sri Lanka]. If you play at Mohali, it is going to be flat, if you play at Wankhede [in Mumbai], it could turn square like here. You can't just have one plan."
Australia last secured a series win in India during the 2004 Border-Gavaskar series. They will enter next year's tour on the back of some poor results in the Indian subcontinent over the years. The Men In Blue have notably secured series wins in their last two visits Down Under as well.
"In a lot of ways sweeps can be blocks over here" - Daniel Vettori on Australia's approach in Sri Lanka
The Australian batters employed a proactive approach against Sri Lanka's spin quatret in Galle last week. They used the sweep shot as a mode for survival as well as a run-scoring option.
The hosts also attempted to use the same approach, but it only paid off for Niroshan Dickwella, who scored a counter-attacking fifty in the first innings.
Speaking about the importance of having a sweep shot in the batting arsenal, Daniel Vettori said:
"In a lot of ways, sweeps can be blocks over here. There have been plans for individuals to use whatever they feel comfortable with, and to be as proactive and brave as they could with it."
"The guys who do sweep very well tried to emphasise that as much as possible. Alex Carey, I think his first 12 scoring shots were sweeps."
Australia will take on Sri Lanka in the final contest of the all-format tour from July 8 onwards. The visitors lead the series 1-0 and could mark their second successive series win on the subcontinent with another win in Galle.